HCF of 40 60 and 75

The HCF of 40, 60 and 75 is 5. The greatest number that divides 40, 60, and 75 exactly, leaving no remainder, is the HCF of these numbers. The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 40, 60 and 75. The factors for 40, 60, and 75 are, (1, 2, 4, 5, 8, 10, 20, 40), (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), and (1, 3, 5, 15, 25, 75), respectively.

Also read: Highest common factor

What is the HCF of 40, 60 and 75?

The answer to this question is 5. This article shows the HCF of 40, 60 and 75 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 40, 60 and 75?

There are three methods to find the HCF of 40, 60 and 75:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 40, 60 and 75 by Prime Factorisation Method

The prime factorisation of 40, 60 and 75 is given by:

Prime factorisation of 40 = (2 × 2 × 2 × 5)

Prime factorisation of 60 = (2 × 2 × 3 × 5)

Prime factorisation of 75 = (3 × 5 × 5)

Hence, the HCF of 40, 60 and 75 is 5.

HCF (40, 60, 75) = 5

HCF of 40, 60 and 75 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 40, 60 and 75.

HCF of 40, 60 and 75
HCF of 40, 60 and 75

No further division can be done.

Hence, HCF (40, 60, 75) = 5

HCF of 40, 60 and 75 by Listing the Factors

To calculate the HCF of 40, 60 and 75 by listing out the common factors, list the factors as shown below:

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

There are 2 common factors of 40, 60 and 75, that are 1 and 5. Therefore, the highest common factor of 40, 60 and 75 is 5

Related Articles

Video Lesson on Properties of HCF and LCM

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.

Frequently Asked Questions on HCF of 40, 60 and 75

Q1

What is the HCF of 40, 60 and 75?

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.
Q2

How to Find the HCF of 40, 60 and 75 by Prime Factorisation?

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.
Q3

What are the Methods to Find HCF of 40, 60 and 75?

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
Q4

Which of the following is HCF of 40, 60 and 75? 5, 120, 79, 111, 117, 79, 115

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.
Q5

What is the Relation Between LCM and HCF of 40, 60 and 75?

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) = [(40 × 60 × 75) × LCM(40, 60, 75)]/[LCM(40, 60) × LCM (60, 75) × LCM(40, 75)].

Comments

Leave a Comment

Your Mobile number and Email id will not be published.

*

*