The HCF of 12 and 16 is 4. HCF stands for Highest Common Factor, and as the name suggests, the number that is highest among the common factors is known as HCF. It can also be referred to as GCD, Greatest Common Divisor or GCF, Greatest Common Factor. For the given set of numbers 12 and 16, 4 is the HCF/GCD/GCF. Even though there are other common factors, like 1 and 2, 4 is greater than the other common factors. You can refer to the Highest Common Factor for more details.
What is the HCF of 12 and 16?
The Highest Common Factor, also known as the Greatest Common Factor, of 12 and 16 is 4.
How to Find HCF of 12 and 16?
There are three methods to find the HCF of 12 and 16:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 12 and 16 by Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 12 and 16 can be expressed as;
12 = 2 × 2 × 3
16 = 2 × 2 × 2 × 2
Common prime factors of 12 and 16 are 2 and 2. Therefore HCF will be,
HCF (12, 16) = 2 × 2 = 4.
HCF of 12 and 16 by Long Division Method
In the Long division method, the following steps are used.
- From the given set of numbers, the smallest number becomes the divisor, and the larger number becomes the dividend.
- In the next step, the smaller number becomes the dividend, and the remainder becomes the divisor.
- The above step is followed until the remainder is zero.
- The last divisor would be the HCF.
For 12 and 16, the HCF by Long Division method is;
HCF (12, 16) = 4
HCF of 12 and 16 by Listing the Factors
By listing all the factors of given numbers, we can identify the highest/greatest/biggest common factor, which is the HCF. Below is the list of factors for 12 and 16.
Factors of 12: 1, 2, 3, 4, 6, and 12
Factors of 16: 1, 2, 4, 8, and 16.
Therefore, HCF (12, 16) = 4
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the greatest number that divides 16 and 64 equally?
Factors of 16 are 1, 2, 4, 8 and 16.
Factors of 64 are 1, 2, 4, 8, 16, 32 and 64.
Common Factors are 1, 2, 4, 8 and 16. The Greatest Common Factor is 16. Hence 16 is the greatest number that divides 16 and 64 equally.
2. What is the GCF of 16 and 8?
GCF of 16 and 8 is 8.
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