HCF of 96 and 72
HCF of 96 and 72 is the largest possible number that divides 96 and 72 exactly without any remainder. The factors of 96 and 72 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 commonly used methods to find the HCF of 96 and 72  prime factorization, Euclidean algorithm, and long division.
1.  HCF of 96 and 72 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 96 and 72?
Answer: HCF of 96 and 72 is 24.
Explanation:
The HCF of two nonzero integers, x(96) and y(72), is the highest positive integer m(24) that divides both x(96) and y(72) without any remainder.
Methods to Find HCF of 96 and 72
Let's look at the different methods for finding the HCF of 96 and 72.
 Listing Common Factors
 Long Division Method
 Prime Factorization Method
HCF of 96 and 72 by Listing Common Factors
 Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
There are 8 common factors of 96 and 72, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the highest common factor of 96 and 72 is 24.
HCF of 96 and 72 by Long Division
HCF of 96 and 72 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 96 (larger number) by 72 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (24).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (24) is the HCF of 96 and 72.
HCF of 96 and 72 by Prime Factorization
Prime factorization of 96 and 72 is (2 × 2 × 2 × 2 × 2 × 3) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 96 and 72 have common prime factors. Hence, the HCF of 96 and 72 is 2 × 2 × 2 × 3 = 24.
☛ Also Check:
 HCF of 120, 144 and 204 = 12
 HCF of 7 and 11 = 1
 HCF of 36 and 42 = 6
 HCF of 140 and 196 = 28
 HCF of 56 and 84 = 28
 HCF of 1872 and 1320 = 24
 HCF of 8 and 12 = 4
HCF of 96 and 72 Examples

Example 1: Find the HCF of 96 and 72, if their LCM is 288.
Solution:
∵ LCM × HCF = 96 × 72
⇒ HCF(96, 72) = (96 × 72)/288 = 24
Therefore, the highest common factor of 96 and 72 is 24. 
Example 2: For two numbers, HCF = 24 and LCM = 288. If one number is 96, find the other number.
Solution:
Given: HCF (x, 96) = 24 and LCM (x, 96) = 288
∵ HCF × LCM = 96 × (x)
⇒ x = (HCF × LCM)/96
⇒ x = (24 × 288)/96
⇒ x = 72
Therefore, the other number is 72. 
Example 3: The product of two numbers is 6912. If their HCF is 24, what is their LCM?
Solution:
Given: HCF = 24 and product of numbers = 6912
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 6912/24
Therefore, the LCM is 288.
FAQs on HCF of 96 and 72
What is the HCF of 96 and 72?
The HCF of 96 and 72 is 24. To calculate the Highest common factor of 96 and 72, we need to factor each number (factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the highest factor that exactly divides both 96 and 72, i.e., 24.
How to Find the HCF of 96 and 72 by Prime Factorization?
To find the HCF of 96 and 72, we will find the prime factorization of the given numbers, i.e. 96 = 2 × 2 × 2 × 2 × 2 × 3; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 96 and 72. Hence, HCF(96, 72) = 2 × 2 × 2 × 3 = 24
☛ What is a Prime Number?
How to Find the HCF of 96 and 72 by Long Division Method?
To find the HCF of 96, 72 using long division method, 96 is divided by 72. The corresponding divisor (24) when remainder equals 0 is taken as HCF.
What are the Methods to Find HCF of 96 and 72?
There are three commonly used methods to find the HCF of 96 and 72.
 By Listing Common Factors
 By Long Division
 By Prime Factorization
What is the Relation Between LCM and HCF of 96, 72?
The following equation can be used to express the relation between Least Common Multiple and HCF of 96 and 72, i.e. HCF × LCM = 96 × 72.
If the HCF of 72 and 96 is 24, Find its LCM.
HCF(72, 96) × LCM(72, 96) = 72 × 96
Since the HCF of 72 and 96 = 24
⇒ 24 × LCM(72, 96) = 6912
Therefore, LCM = 288
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