HCF of 24 and 32

HCF of 24 and 32: HCF (Highest Common Factor) is also called Highest Common Divisor or Greatest Common Measure (GCM). HCF is the highest number that can divide two or more numbers equally and entirely. If c and d are two numbers given then the HCF of c and d is the number that divides them entirely and is the higher of all the divisors.

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What Is the HCF of the 24 and 32?

There are many methods to find the HCF of numbers:

• Listing Factor Method
• Prime Factorization Method
• Division Method

Let us look at each method:

HCF of 24 and 32 Using the Listing Factor Method

The listing factor method is one of the simple and basically used methods to find the HCF of any given number.

Step 1: Write the factors of each given number.

Step 2: Find the common factors in the given numbers.

Step 3: Find the highest factor in the common factors which is HCF.

Therefore, the HCF of 24 and 32 using the listing method are as follows:
Step 1: Find the factors 24 and 32.
The factor of 24= 1,2,3,4,6,8,12 and 24
The factor of 32=1,2,4,8,16 and 32
Step 2: Write the common factors

HCF of 24 and 32 Using Prime Factorization Method

Step 1: Find the prime factors for the given numbers
The prime factor of 24 = 2✕2✕2The prime factor of 32 =2✕2✕2✕2✕2
Step 2: Find the common prime factors of the given number
The common prime factors in the given number are 2✕2✕2
Step 3: Find the highest prime number. Which is the HCF of the given number.
The highest prime number = 8
Hence, the HCF of (6,12)=8.

HCF of 24 and 32 Using Division Method

In the division method, the following step is considered to know the HCF of the given numbers.
Step 1: For the given numbers divide the smallest number by the largest number.
Step 2: Continue the division with the quotient and the remainder until it achieves zero
Step 3: once zero is reached the last divisor in which it was attained is the HCF of the given numbers.
Therefore, the HCF for 24 and 32 using the division method:
Step 1: For the given numbers divide the smallest number by the largest number.
Step 2: Continue the division with the quotient and the remainder until it achieves zero
Step 3: once zero is reached the last divisor in which it was attained is the HCF of the given numbers.
The last divisor is 8
Hence, the HCF of (24,32)=8

Solved Examples:

Example 1: What are the HCF and LCM of 24 and 32?
The HCF of (24,32)=8
The LCM of (24,32)= 96

Example 2: What is the HCF of 25 and 32?
The factor of 25=1,5&25
The factor of 32=1, 2, 4, 8, 16, 32, 64
Hence the HCF of  (25,32)= 1

Example 3: What is the HCF of 24 and 30?
The prime factor of 24=2✕2✕2✕3
The prime factor of 30=2✕3✕5
The HCF of (24,30)=6

Example 4: What is the HCF of 24 16 and 32?
The factor of 24= 1,2,3,4,6,8,12 and 24
The factor of 32=1,2,4,8,16 and 32
The factor of 16=1, 2, 4, 8, and 16.
The HCF of (24,16,32)= 8

Example 5: What is the HCF of 24 and 32 if their LCM is 96?
The HCF of (24,32)=8 if their LCM is 96.

Example 6: Find the HCF of 6 and 12.
Let us find using these simple steps:
Step 1: Find the factors 6 and 12
The factor 6= 1,2,3 and 6
The factor 12=1,2,3,4,6 and 12
Step 2: Write the common factors
The common factors are=1,2,3 and 6
Step 3: Find the highest common factor
The highest common factor is 6
Hence, HCF of (6,12)=6

Example 7: Find the HCF of 6 and 12 using the prime factorization method.
Step1: Find the prime factors for the given numbers
The prime factor of 6= 2✕3
The prime factor of 12= 2✕2✕3
Step 2: Find the common prime factors of the given number
The common prime factor numbers are 2 ✕3
Step 3: Find the highest prime number by multiplying the common factors. Which is the HCF of the given number.
The highest prime number is 6
Hence, the HCF of (6,12)=6

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FAQ

What is HCF?
HCF is the highest common number that divides two or more given numbers entirely.

How many methods are there to find HCF?
There are three methods to find the HCF of numbers namely the factorization method, Prime factorization method, and long division method.

What are the factors of 24?
The factors of 24 are 1,2,3,4,6,8,12 and 24.

Are the factorization and prime factorization methods the same?
No, they are different factors that can be any number that is multiplied to achieve the given number, whereas, prime factors use only prime numbers to multiply the given number.

What is the prime factor of 32?
The prime factors of 32 are 2✕2✕2✕2✕2.

What is the HCF of 24 & 32?
The HCF of 24 &32 is 8