HCF of 24 and 32
HCF of 24 and 32 is the largest possible number that divides 24 and 32 exactly without any remainder. The factors of 24 and 32 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 4, 8, 16, 32 respectively. There are 3 commonly used methods to find the HCF of 24 and 32  long division, Euclidean algorithm, and prime factorization.
1.  HCF of 24 and 32 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 24 and 32?
Answer: HCF of 24 and 32 is 8.
Explanation:
The HCF of two nonzero integers, x(24) and y(32), is the highest positive integer m(8) that divides both x(24) and y(32) without any remainder.
Methods to Find HCF of 24 and 32
Let's look at the different methods for finding the HCF of 24 and 32.
 Prime Factorization Method
 Long Division Method
 Listing Common Factors
HCF of 24 and 32 by Prime Factorization
Prime factorization of 24 and 32 is (2 × 2 × 2 × 3) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 24 and 32 have common prime factors. Hence, the HCF of 24 and 32 is 2 × 2 × 2 = 8.
HCF of 24 and 32 by Long Division
HCF of 24 and 32 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 32 (larger number) by 24 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (8).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (8) is the HCF of 24 and 32.
HCF of 24 and 32 by Listing Common Factors
 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
 Factors of 32: 1, 2, 4, 8, 16, 32
There are 4 common factors of 24 and 32, that are 8, 1, 2, and 4. Therefore, the highest common factor of 24 and 32 is 8.
☛ Also Check:
 HCF of 2 and 3 = 1
 HCF of 108 and 144 = 36
 HCF of 1095 and 1168 = 73
 HCF of 14 and 15 = 1
 HCF of 398, 436 and 542 = 2
 HCF of 6, 72 and 120 = 6
 HCF of 34 and 102 = 34
HCF of 24 and 32 Examples

Example 1: The product of two numbers is 768. If their HCF is 8, what is their LCM?
Solution:
Given: HCF = 8 and product of numbers = 768
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 768/8
Therefore, the LCM is 96. 
Example 2: For two numbers, HCF = 8 and LCM = 96. If one number is 32, find the other number.
Solution:
Given: HCF (y, 32) = 8 and LCM (y, 32) = 96
∵ HCF × LCM = 32 × (y)
⇒ y = (HCF × LCM)/32
⇒ y = (8 × 96)/32
⇒ y = 24
Therefore, the other number is 24. 
Example 3: Find the HCF of 24 and 32, if their LCM is 96.
Solution:
∵ LCM × HCF = 24 × 32
⇒ HCF(24, 32) = (24 × 32)/96 = 8
Therefore, the highest common factor of 24 and 32 is 8.
FAQs on HCF of 24 and 32
What is the HCF of 24 and 32?
The HCF of 24 and 32 is 8. To calculate the Highest common factor of 24 and 32, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 32 = 1, 2, 4, 8, 16, 32) and choose the highest factor that exactly divides both 24 and 32, i.e., 8.
If the HCF of 32 and 24 is 8, Find its LCM.
HCF(32, 24) × LCM(32, 24) = 32 × 24
Since the HCF of 32 and 24 = 8
⇒ 8 × LCM(32, 24) = 768
Therefore, LCM = 96
☛ HCF Calculator
What is the Relation Between LCM and HCF of 24, 32?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 24 and 32, i.e. HCF × LCM = 24 × 32.
How to Find the HCF of 24 and 32 by Long Division Method?
To find the HCF of 24, 32 using long division method, 32 is divided by 24. The corresponding divisor (8) when remainder equals 0 is taken as HCF.
How to Find the HCF of 24 and 32 by Prime Factorization?
To find the HCF of 24 and 32, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 24 and 32. Hence, HCF(24, 32) = 2 × 2 × 2 = 8
☛ What is a Prime Number?
What are the Methods to Find HCF of 24 and 32?
There are three commonly used methods to find the HCF of 24 and 32.
 By Prime Factorization
 By Long Division
 By Listing Common Factors