## What Is The Highest Common Factor?

Contents

- 1 What is difference between LCM and HCF?
- 2 What is the HCF of 12 and 24?
- 3 Why do we use HCF?
- 4 What is the HCF of 45 and 60?
- 5 What is HCF and LCM for dummies?
- 6 Is HCF and HCF the same?
- 7 Is HCF always a factor of LCM?
- 8 What is HCF of 40?
- 9 Is 13 a multiple of 3?
- 10 What is the LCM of 8 and 10?
- 11 What is the HCF of 6 and 10?

### What is a highest common factor in math?

How do the highest common factors relate to other areas of maths? – The highest common factors are useful when simplifying and comparing fractions. If you can work out the highest common factor of the numerator (top number) and the denominator (bottom number), you can express the fraction in its simplest form (a skill required in Year 6).

### What is meant by HCF?

widgets-close-button HCF or Highest Common Factor is the greatest number which divides each of the two or more numbers. HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor(GCD), are two different methods, where LCM or Least Common Multiple is used to find the smallest common multiple of any two or more numbers.

## What is difference between LCM and HCF?

HCF and LCM (Definition, Formulas & Examples) The full form of LCM in Maths is the Least Common Multiple, whereas the full form of HCF is the Highest Common Factor. The H.C.F. defines the greatest factor present in between given two or more numbers, whereas L.C.M.

- Defines the least number which is exactly divisible by two or more numbers.H.C.F.
- Is also called the and LCM is also called the Least Common Divisor.
- To find H.C.F.
- And L.C.M., we have two important methods which are the Prime factorization method and the division method.
- We have learned both methods in our earlier classes.

The shortcut method to find both H.C.F. and L.C.M. is a division method. Let us learn the with the help of the formula here. Also, we will solve some problems based on these two concepts to understand in a better way. The article here is very helpful for primary and secondary classes students such as Class 4, Class 5, Class 6, Class 7, and Class 8.

#### What is the HCF of 24 and 36?

HCF of 24 and 36 | How to Find HCF of 24 and 36 The HCF of 24 and 36 is 12. HCF is the greatest number that can divide 24 and 36 without having any remainder. HCF stands for Highest Common Factor. As the name suggests, for a given set of numbers 24 and 36, there would be common factors, and the highest among the common factors is known as the HCF.

## What is the HCF of 12 and 24?

What is the HCF of 12 and 24? – The Highest Common Factor of 12 and 24 is 12. There are six common factors of 12 and 24. They are 1, 2, 3, 4, 6, and 12. Here, 12 is the largest number. Hence the Highest Common Factor of 12 and 24 is 12.

## Why do we use HCF?

What are the Applications of LCM and HCF? – LCM (Least Common Multiple) and HCF (Highest Common Factor) are two mathematical concepts that are used extensively in many different areas of mathematics. One of the primary applications of LCM is in finding the lowest common denominator (LCD) of two or more fractions.

The LCD is the smallest number that is a multiple of all of the given fractions. For example, if you are trying to add the fractions ¾ and 2/9, the LCD would be 36 because 36 is a multiple of both 3 and 6. HCF is used extensively in algebra, where it is often used to simplify polynomial equations. It can also be used to find the greatest common factor (GCF) of two or more numbers.

The GCF is the largest number that is a factor of all of the given numbers. LCM and HCF The LCM of two numbers is the smallest number that is divisible by both numbers. The HCF of two numbers is the largest number that is divisible by both numbers. September, 2023 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

## What is the HCF of 45 and 60?

GCF of 45 and 60 by Listing Common Factors –

- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There are 4 common factors of 45 and 60, that are 1, 3, 5, and 15. Therefore, the greatest common factor of 45 and 60 is 15. ☛ Also Check:

- GCF of 48 and 56 = 8
- GCF of 22 and 44 = 22
- GCF of 44 and 66 = 22
- GCF of 26 and 91 = 13
- GCF of 12 and 27 = 3
- GCF of 60 and 90 = 30
- GCF of 30 and 60 = 30

## What is HCF and LCM for dummies?

Difference between HCF and LCM –

HCF | LCM |
---|---|

It is the Highest Common Factor. | It is the Least Common Multiple. |

The greatest of all the common factors among the given numbers is HCF. | The smallest of all the common multiples among the given numbers is LCM. |

The HCF of given numbers will never be greater than any of the numbers. | The LCM of the given numbers will always be greater than the numbers given. |

#### What is HCF of 24 and 32?

HCF of 24 and 32 | How to Find HCF of 24 and 32 The HCF of 24 and 32 is 8. The numbers 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 4, 8, 16, 32 are the factors of 24 and 32, respectively. Among these factors, 8 is the highest number that exactly divides the numbers 24 and 32.

## Is HCF and HCF the same?

Q) What is HCF? – HCF stands for Highest Common Factor. It is the largest value of factor that can be obtained from the common factors of two or more given numbers. It is also known by other names as GCF (Greatest Common Factor) or GCD (Greatest Common Divisor) or GCM (Greatest Common Measure).

#### Is the HCF always the LCM?

Hence, the statement ‘ HCF of two numbers is always a factor of their LCM ‘ is true.

#### Is HCF always greater than LCM?

Additional Information: HCF of two numbers is always less than or equal to their LCM.

## Is HCF always a factor of LCM?

Hint: Basics of H.C.F and L.C.M. : $\left( 1 \right)$ H.C.F. ( highest common factor ) : H.C.F. is also called the greatest common factor ( G.C.F.) and it is defined as the highest or largest number which divides the given two or more numbers completely means there must be no remainder.

Left( 2 \right)$ L.C.M. ( lowest common multiple ) : It is defined as the lowest or smallest common multiple of the given two or more numbers. There are two methods which are used to find the H.C.F and L.C.M. commonly: $\left( } \right)$ Prime factorization method and $\left( }} \right)$ Long division method.

Complete step-by-step solution: Let us discuss the prime factorization method to find H.C.F. and L.C.M. : $\left( 1 \right)$ H.C.F. by prime factorization method: Let us understand the concept with an example ; Find the H.C.F. of $24 }$ $?$ The steps are as follows :- Step $1$ : Find the prime factors of the given numbers.

- } = 2 \times 2 \times 2 \times 3 \times 1 = \times 3 \times 1$ $ } = 2 \times 2 \times 3 \times 1 = \times 3 \times 1$ Step $2$ : List the common factors and the product of least powers of common prime factors gives the H.C.F.
- Rightarrow 24 = \times \times 1$ $ \Rightarrow 12 = \times \times 1$ Since $2$ is common in both and it’s least power is $ $ and $3$ is also common with least power as $ $ ; H.C.F.

$\left( \right) \Rightarrow \times \times 1 = 12$ $\left( 2 \right)$ L.C.M. by prime factorization method: Let us understand the concept with the same example ; Step $1$ : Find the prime factors of the given numbers. $ } = 2 \times 2 \times 2 \times 3 \times 1 = \times 3 \times 1$ $ } = 2 \times 2 \times 3 \times 1 = \times 3 \times 1$ Step $2$ : List the common factors and the product of highest powers of common prime factors and the remaining prime factors gives the L.C.M.

- Rightarrow 24 = \times \times 1$ $ \Rightarrow 12 = \times \times 1$ Since $2$ is common in both and it’s highest power is $ $ and $3$ is also common with highest power as $ $ ; L.C.M.
- Left( \right) \Rightarrow \times \times 1 = 24$ Now, let us come to our question; Statement: H.C.F.
- Of two numbers is always a factor of their L.C.M.

( True/False) $?$ Let us take some examples and try to analyze this statement ; $\left( 1 \right)$ Find L.C.M. and H.C.F. of $\left( \right)$ : Step $1$ : $ } = 2 \times 13 \times 1$ $ } = 7 \times 13 \times 1$ Step $2$ : $26 = \times \times 1$ \ L.C.M.

- Rightarrow \times 2 \times 7 \times 1 = 182$ H.C.F.
- Rightarrow \times 1 = 13$ Conclusion: Here, we notice that L.C.M.
- = 182$ and H.C.F.
- = 13$ means $182$ is completely divisible by $13$,
- Hence we can say that H.C.F.
- Is a factor of the L.C.M.
- Left( 2 \right)$ Find L.C.M.
- And H.C.F.
- Of $\left( \right)$ : Step $1$ : $ } = 2 \times 2 \times 2 \times 3 \times 1 = \times \times 1$ $ } = 2 \times 2 \times 2 \times 2 \times 2 \times 1 = \times 1$ $ } = 2 \times 3 \times 3 \times 3 \times 1 = \times \times 1$ Step $2$ : $24 = \times \times 1$ \ \ L.C.M.

$ \Rightarrow \times \times 1 = 864$ H.C.F. $ \Rightarrow 2 \times 1 = 2$ Conclusion: Here, we notice that L.C.M. $ = 864$ and H.C.F. $ = 2$ means $864$ is completely divisible by $2$, Hence we can say that H.C.F. is a factor of the L.C.M. So, with the help of above examples we have proved that the given statement “H.C.F.

- Of two numbers is always a factor of their L.C.M.” is true.
- Note: The important relation between H.C.F.
- And L.C.M.
- Is : The product of H.C.F.
- And L.C.M.
- Of two numbers is equivalent to the product of the given two numbers and this relation is very useful while solving questions.
- Example : For two numbers $\left( \right); } } } } } } }$ ; then $26 \times 91 = 13 \times 182 = 2366$,

However, this relation fails in the case of three numbers.

## What is HCF of 40?

HCF of 40, 60 and 75 Solved Example –

- Find the highest number that divides 40, 60, and 75 completely.
- Solution:
- The highest number that divides 40, 60, and 75 exactly is their highest common factor.
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 75 = 1, 3, 5, 15, 25, 75
- The HCF of 40, 60, and 75 is 5.
- The highest number that divides 40, 60, and 75 is 5.

The HCF of 40, 60 and 75 is 5. To calculate the highest common factor of 40, 60 and 75, we need to factor each number and choose the highest factor that exactly divides 40, 60 and 75, i.e., 5. To find the HCF of 40, 60 and 75, we will find the prime factorization of given numbers, i.e.40 = 2 × 2 × 2 × 5; 60 = 2 × 2 × 3 × 5; 75 = 3 × 5 × 5.

- Since 5 is the only common prime factor of 40, 60 and 75.
- Hence, HCF(40, 60, 75) = 5.
- There are three commonly used methods to find the HCF of 40, 60 and 75.
- By Long Division By Listing Common Factors By Prime Factorisation HCF of 40, 60, 75 will be the number that divides 40, 60, and 75 without leaving any remainder.

The only number that satisfies the given condition is 5. The following equation can be used to express the relation between LCM and HCF of 40, 60 and 75, i.e. HCF(40, 60, 75) = /. : HCF of 40, 60 and 75 | How to Find HCF of 40, 60 and 75

## Is 13 a multiple of 3?

No, 13 is not a multiple of 3.

#### What is the LCM of 6 and 8?

LCM of 6 and 8 | How to Find LCM of 6 and 8 LCM of 6 and 8 is 24. The least common multiple is the process to find the smallest common multiple between any two or more numbers. It is also used to add or subtract any two fractions when the denominators of the fraction are different.

## What is the LCM of 8 and 10?

What is the LCM of 8 and 10? The LCM of 8 and 10 is 40.

### What is the HCF of 7 and 11?

The HCF of 7 and 11 is 1. The common factor for 7 and 11 is 1. Hence, HCF is 1.

#### What is the HCF of 12 and 18?

The HCF of 12 and 18 is 6.

#### What is the HCF of 12 and 15?

HCF of 12 and 15 | How to Find HCF of 12 and 15 The HCF of 12 and 15 is 3, HCF stands for Highest common factor, and as the name suggests, the number that is highest among the common factors is known as HCF. It can also be referred to as GCD, Greatest Common Divisor or GCF, Greatest Common Factor.

## What is the HCF of 6 and 10?

HCF of 6 and 10 | How to Find HCF of 6 and 10 The HCF of 6 and 10 is 2, HCF of 6 and 10 is the greatest integer that can divide both numbers evenly, and that number is 2. HCF stands for Highest Common Factor, and it is also known as GCF, Greatest Common Factor or GCD, Greatest Common Divisor.