A day full of math games & activities. Find one near you.

HCF of 32 and 60

HCF of 32 and 60 is the largest possible number that divides 32 and 60 exactly without any remainder. The 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. There are 3 commonly used methods to find the HCF of 32 and 60 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 32 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 32 and 60?

Answer: HCF of 32 and 60 is 4.

Explanation:

The HCF of two non-zero integers, x(32) and y(60), is the highest positive integer m(4) that divides both x(32) and y(60) without any remainder.

Methods to Find HCF of 32 and 60

The methods to find the HCF of 32 and 60 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

HCF of 32 and 60 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 60 and Y = 32

HCF(60, 32) = HCF(32, 60 mod 32) = HCF(32, 28)
HCF(32, 28) = HCF(28, 32 mod 28) = HCF(28, 4)
HCF(28, 4) = HCF(4, 28 mod 4) = HCF(4, 0)
HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 32 and 60 is 4.

HCF of 32 and 60 by Prime Factorization

Prime factorization of 32 and 60 is (2 × 2 × 2 × 2 × 2) and (2 × 2 × 3 × 5) respectively. As visible, 32 and 60 have common prime factors. Hence, the HCF of 32 and 60 is 2 × 2 = 4.

HCF of 32 and 60 by Long Division

HCF of 32 and 60 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 60 (larger number) by 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (28).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 32 and 60.

☛ Also Check:

HCF of 32 and 60 Examples

Example 1: The product of two numbers is 1920. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 1920
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1920/4
Therefore, the LCM is 480.
Example 2: Find the highest number that divides 32 and 60 exactly.

Solution:

The highest number that divides 32 and 60 exactly is their highest common factor, i.e. HCF of 32 and 60.
⇒ Factors of 32 and 60:
- 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.
Example 3: For two numbers, HCF = 4 and LCM = 480. If one number is 32, find the other number.

Solution:

Given: HCF (z, 32) = 4 and LCM (z, 32) = 480
∵ HCF × LCM = 32 × (z)
⇒ z = (HCF × LCM)/32
⇒ z = (4 × 480)/32
⇒ z = 60
Therefore, the other number is 60.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on HCF of 32 and 60

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 (factors of 32 = 1, 2, 4, 8, 16, 32; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the highest factor that exactly divides both 32 and 60, i.e., 4.

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

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
☛ Prime Numbers

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 Euclidean Algorithm
By Prime Factorization

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.

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.

If the HCF of 60 and 32 is 4, Find its LCM.

HCF(60, 32) × LCM(60, 32) = 60 × 32
Since the HCF of 60 and 32 = 4
⇒ 4 × LCM(60, 32) = 1920
Therefore, LCM = 480
☛ HCF Calculator

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum