HCF of 6 and 24
HCF of 6 and 24 is the largest possible number that divides 6 and 24 exactly without any remainder. The factors of 6 and 24 are 1, 2, 3, 6 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the HCF of 6 and 24  prime factorization, Euclidean algorithm, and long division.
1.  HCF of 6 and 24 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 6 and 24?
Answer: HCF of 6 and 24 is 6.
Explanation:
The HCF of two nonzero integers, x(6) and y(24), is the highest positive integer m(6) that divides both x(6) and y(24) without any remainder.
Methods to Find HCF of 6 and 24
The methods to find the HCF of 6 and 24 are explained below.
 Long Division Method
 Using Euclid's Algorithm
 Prime Factorization Method
HCF of 6 and 24 by Long Division
HCF of 6 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 24 (larger number) by 6 (smaller number).
 Step 2: Since the remainder = 0, the divisor (6) is the HCF of 6 and 24.
The corresponding divisor (6) is the HCF of 6 and 24.
HCF of 6 and 24 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 = 24 and Y = 6
 HCF(24, 6) = HCF(6, 24 mod 6) = HCF(6, 0)
 HCF(6, 0) = 6 (∵ HCF(X, 0) = X, where X ≠ 0)
Therefore, the value of HCF of 6 and 24 is 6.
HCF of 6 and 24 by Prime Factorization
Prime factorization of 6 and 24 is (2 × 3) and (2 × 2 × 2 × 3) respectively. As visible, 6 and 24 have common prime factors. Hence, the HCF of 6 and 24 is 2 × 3 = 6.
☛ Also Check:
 HCF of 117 and 221 = 13
 HCF of 10224 and 9648 = 144
 HCF of 1872 and 1320 = 24
 HCF of 20, 28 and 36 = 4
 HCF of 4 and 6 = 2
 HCF of 144 and 198 = 18
 HCF of 120 and 144 = 24
HCF of 6 and 24 Examples

Example 1: Find the highest number that divides 6 and 24 exactly.
Solution:
The highest number that divides 6 and 24 exactly is their highest common factor, i.e. HCF of 6 and 24.
⇒ Factors of 6 and 24: Factors of 6 = 1, 2, 3, 6
 Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the HCF of 6 and 24 is 6.

Example 2: Find the HCF of 6 and 24, if their LCM is 24.
Solution:
∵ LCM × HCF = 6 × 24
⇒ HCF(6, 24) = (6 × 24)/24 = 6
Therefore, the highest common factor of 6 and 24 is 6. 
Example 3: For two numbers, HCF = 6 and LCM = 24. If one number is 24, find the other number.
Solution:
Given: HCF (x, 24) = 6 and LCM (x, 24) = 24
∵ HCF × LCM = 24 × (x)
⇒ x = (HCF × LCM)/24
⇒ x = (6 × 24)/24
⇒ x = 6
Therefore, the other number is 6.
FAQs on HCF of 6 and 24
What is the HCF of 6 and 24?
The HCF of 6 and 24 is 6. To calculate the HCF of 6 and 24, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the highest factor that exactly divides both 6 and 24, i.e., 6.
How to Find the HCF of 6 and 24 by Prime Factorization?
To find the HCF of 6 and 24, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 24 = 2 × 2 × 2 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 6 and 24. Hence, HCF(6, 24) = 2 × 3 = 6
☛ What are Prime Numbers?
What is the Relation Between LCM and HCF of 6, 24?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 6 and 24, i.e. HCF × LCM = 6 × 24.
How to Find the HCF of 6 and 24 by Long Division Method?
To find the HCF of 6, 24 using long division method, 24 is divided by 6. The corresponding divisor (6) when remainder equals 0 is taken as HCF.
If the HCF of 24 and 6 is 6, Find its LCM.
HCF(24, 6) × LCM(24, 6) = 24 × 6
Since the HCF of 24 and 6 = 6
⇒ 6 × LCM(24, 6) = 144
Therefore, LCM = 24
☛ HCF Calculator
What are the Methods to Find HCF of 6 and 24?
There are three commonly used methods to find the HCF of 6 and 24.
 By Long Division
 By Listing Common Factors
 By Prime Factorization
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