HCF of 32 and 60

The HCF of 32 and 60 is 4. HCF of 32 and 60 is the biggest number that can divide those two numbers perfectly, leaving no residue. Factors of 32 and 60 are 1, 2, 4, 8, 16, 32 and 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, respectively. The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 32 and 60.

Also read: Highest common factor

What is the HCF of 32 and 60?

The answer to this question is 4. This article shows the HCF of 32 and 60 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 32 and 60?

There are three methods to find the HCF of 32 and 60:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 32 and 60 by Prime Factorisation Method

The prime factorisation of 32 and 60 is given by:

Prime factorisation of 32 = (2 × 2 × 2 × 2 × 2)

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

Hence, the HCF of 32 and 60 is 2 × 2 = 4.

HCF (32, 60) = 4

HCF of 32 and 60 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 32 and 60.

HCF of 32 and 60

No further division can be done.

Hence, HCF (32, 60) = 4

HCF of 32 and 60 by Listing the Factors

To calculate the HCF of 32 and 60 by listing out the common factors, list the factors as shown below:

Factors of 32 = 1, 2, 4, 8, 16, 32

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Therefore, the HCF of 32 and 60 is 4.

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Video Lesson on Properties of HCF and LCM

HCF of 32 and 60 Solved Example

For two numbers, HCF = 4 and LCM = 480. If one number is 32, find the other number.

Solution:

Given: HCF (x, 32) = 4 and LCM (x, 32) = 480

We have HCF × LCM = 32 × (z)

⇒ x = (HCF × LCM)/32

⇒ x = (4 × 480)/32

⇒ x = 60

Therefore, the other number is 60.

Frequently Asked Questions on HCF of 32 and 60

Q1

What is the HCF of 32 and 60?

The HCF of 32 and 60 is 4. To calculate the HCF (Highest Common Factor) of 32 and 60, we need to factor each number and choose the highest factor that exactly divides both 32 and 60, i.e., 4.
Q2

How to Find the HCF of 32 and 60 by Prime Factorisation?

To find the HCF of 32 and 60, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 32 and 60. Hence, HCF(32, 60) = 2 × 2 = 4
Q3

What are the Methods to Find HCF of 32 and 60?

There are three commonly used methods to find the HCF of 32 and 60.
By Long Division
By Listing Common Factors
By Prime Factorisation
Q4

What is the Relation Between LCM and HCF of 32, 60?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 32 and 60, i.e. HCF × LCM = 32 × 60.
Q5

How to Find the HCF of 32 and 60 by Long Division Method?

To find the HCF of 32, 60 using long division method, 60 is divided by 32. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

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