HCF of 72 and 84
HCF of 72 and 84 is the largest possible number that divides 72 and 84 exactly without any remainder. The factors of 72 and 84 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 respectively. There are 3 commonly used methods to find the HCF of 72 and 84  Euclidean algorithm, prime factorization, and long division.
1.  HCF of 72 and 84 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 72 and 84?
Answer: HCF of 72 and 84 is 12.
Explanation:
The HCF of two nonzero integers, x(72) and y(84), is the highest positive integer m(12) that divides both x(72) and y(84) without any remainder.
Methods to Find HCF of 72 and 84
The methods to find the HCF of 72 and 84 are explained below.
 Listing Common Factors
 Prime Factorization Method
 Long Division Method
HCF of 72 and 84 by Listing Common Factors
 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
 Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
There are 6 common factors of 72 and 84, that are 1, 2, 3, 4, 6, and 12. Therefore, the highest common factor of 72 and 84 is 12.
HCF of 72 and 84 by Prime Factorization
Prime factorization of 72 and 84 is (2 × 2 × 2 × 3 × 3) and (2 × 2 × 3 × 7) respectively. As visible, 72 and 84 have common prime factors. Hence, the HCF of 72 and 84 is 2 × 2 × 3 = 12.
HCF of 72 and 84 by Long Division
HCF of 72 and 84 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 84 (larger number) by 72 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (12).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (12) is the HCF of 72 and 84.
☛ Also Check:
 HCF of 36 and 42 = 6
 HCF of 1 and 3 = 1
 HCF of 777 and 1147 = 37
 HCF of 18 and 54 = 18
 HCF of 18 and 24 = 6
 HCF of 10, 20 and 30 = 10
 HCF of 612 and 1314 = 18
HCF of 72 and 84 Examples

Example 1: For two numbers, HCF = 12 and LCM = 504. If one number is 72, find the other number.
Solution:
Given: HCF (z, 72) = 12 and LCM (z, 72) = 504
∵ HCF × LCM = 72 × (z)
⇒ z = (HCF × LCM)/72
⇒ z = (12 × 504)/72
⇒ z = 84
Therefore, the other number is 84. 
Example 2: Find the highest number that divides 72 and 84 exactly.
Solution:
The highest number that divides 72 and 84 exactly is their highest common factor, i.e. HCF of 72 and 84.
⇒ Factors of 72 and 84: Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
 Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Therefore, the HCF of 72 and 84 is 12.

Example 3: Find the HCF of 72 and 84, if their LCM is 504.
Solution:
∵ LCM × HCF = 72 × 84
⇒ HCF(72, 84) = (72 × 84)/504 = 12
Therefore, the highest common factor of 72 and 84 is 12.
FAQs on HCF of 72 and 84
What is the HCF of 72 and 84?
The HCF of 72 and 84 is 12. To calculate the Highest common factor (HCF) of 72 and 84, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84) and choose the highest factor that exactly divides both 72 and 84, i.e., 12.
How to Find the HCF of 72 and 84 by Prime Factorization?
To find the HCF of 72 and 84, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 84 = 2 × 2 × 3 × 7.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 72 and 84. Hence, HCF(72, 84) = 2 × 2 × 3 = 12
☛ What are Prime Numbers?
How to Find the HCF of 72 and 84 by Long Division Method?
To find the HCF of 72, 84 using long division method, 84 is divided by 72. The corresponding divisor (12) when remainder equals 0 is taken as HCF.
What are the Methods to Find HCF of 72 and 84?
There are three commonly used methods to find the HCF of 72 and 84.
 By Prime Factorization
 By Long Division
 By Euclidean Algorithm
What is the Relation Between LCM and HCF of 72, 84?
The following equation can be used to express the relation between Least Common Multiple and HCF of 72 and 84, i.e. HCF × LCM = 72 × 84.
If the HCF of 84 and 72 is 12, Find its LCM.
HCF(84, 72) × LCM(84, 72) = 84 × 72
Since the HCF of 84 and 72 = 12
⇒ 12 × LCM(84, 72) = 6048
Therefore, LCM = 504
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