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 nonzero 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 2 and 3 = 1
 HCF of 960 and 432 = 48
 HCF of 1 and 3 = 1
 HCF of 28 and 36 = 4
 HCF of 12, 16 and 24 = 4
 HCF of 12, 16 and 28 = 4
 HCF of 14 and 15 = 1
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.
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
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