HCF of 84 and 96
HCF of 84 and 96 is the largest possible number that divides 84 and 96 exactly without any remainder. The factors of 84 and 96 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 respectively. There are 3 commonly used methods to find the HCF of 84 and 96  Euclidean algorithm, long division, and prime factorization.
1.  HCF of 84 and 96 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 84 and 96?
Answer: HCF of 84 and 96 is 12.
Explanation:
The HCF of two nonzero integers, x(84) and y(96), is the highest positive integer m(12) that divides both x(84) and y(96) without any remainder.
Methods to Find HCF of 84 and 96
The methods to find the HCF of 84 and 96 are explained below.
 Using Euclid's Algorithm
 Long Division Method
 Listing Common Factors
HCF of 84 and 96 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 = 96 and Y = 84
 HCF(96, 84) = HCF(84, 96 mod 84) = HCF(84, 12)
 HCF(84, 12) = HCF(12, 84 mod 12) = HCF(12, 0)
 HCF(12, 0) = 12 (∵ HCF(X, 0) = X, where X ≠ 0)
Therefore, the value of HCF of 84 and 96 is 12.
HCF of 84 and 96 by Long Division
HCF of 84 and 96 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 96 (larger number) by 84 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (84) by the remainder (12).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (12) is the HCF of 84 and 96.
HCF of 84 and 96 by Listing Common Factors
 Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
 Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
There are 6 common factors of 84 and 96, that are 1, 2, 3, 4, 6, and 12. Therefore, the highest common factor of 84 and 96 is 12.
☛ Also Check:
 HCF of 150 and 225 = 75
 HCF of 144 and 192 = 48
 HCF of 6 and 10 = 2
 HCF of 4 and 8 = 4
 HCF of 14 and 15 = 1
 HCF of 10 and 15 = 5
 HCF of 12, 45 and 75 = 3
HCF of 84 and 96 Examples

Example 1: The product of two numbers is 8064. If their HCF is 12, what is their LCM?
Solution:
Given: HCF = 12 and product of numbers = 8064
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 8064/12
Therefore, the LCM is 672. 
Example 2: Find the highest number that divides 84 and 96 exactly.
Solution:
The highest number that divides 84 and 96 exactly is their highest common factor, i.e. HCF of 84 and 96.
⇒ Factors of 84 and 96: Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
 Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Therefore, the HCF of 84 and 96 is 12.

Example 3: Find the HCF of 84 and 96, if their LCM is 672.
Solution:
∵ LCM × HCF = 84 × 96
⇒ HCF(84, 96) = (84 × 96)/672 = 12
Therefore, the highest common factor of 84 and 96 is 12.
FAQs on HCF of 84 and 96
What is the HCF of 84 and 96?
The HCF of 84 and 96 is 12. To calculate the HCF of 84 and 96, we need to factor each number (factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84; factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and choose the highest factor that exactly divides both 84 and 96, i.e., 12.
How to Find the HCF of 84 and 96 by Prime Factorization?
To find the HCF of 84 and 96, we will find the prime factorization of the given numbers, i.e. 84 = 2 × 2 × 3 × 7; 96 = 2 × 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 84 and 96. Hence, HCF(84, 96) = 2 × 2 × 3 = 12
☛ What is a Prime Number?
What is the Relation Between LCM and HCF of 84, 96?
The following equation can be used to express the relation between Least Common Multiple and HCF of 84 and 96, i.e. HCF × LCM = 84 × 96.
What are the Methods to Find HCF of 84 and 96?
There are three commonly used methods to find the HCF of 84 and 96.
 By Euclidean Algorithm
 By Prime Factorization
 By Long Division
How to Find the HCF of 84 and 96 by Long Division Method?
To find the HCF of 84, 96 using long division method, 96 is divided by 84. The corresponding divisor (12) when remainder equals 0 is taken as HCF.
If the HCF of 96 and 84 is 12, Find its LCM.
HCF(96, 84) × LCM(96, 84) = 96 × 84
Since the HCF of 96 and 84 = 12
⇒ 12 × LCM(96, 84) = 8064
Therefore, LCM = 672
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