HCF of 12 and 15 - Methods and Solved Examples - Testbook

The Highest Common Factor (HCF) of 12 and 15 is 3. The HCF, also known as the Greatest Common Divisor (GCD) or the Greatest Common Factor (GCF), is the largest number that can evenly divide a set of numbers. In this case, the HCF of 12 and 15 is 3, as both 12 and 15 have only two common factors - 1 and 3, with 3 being the highest. For more information, you can visit the Highest Common Factor page.

How to Calculate the HCF of 12 and 15?

There are a few methods to find the HCF of 12 and 15, including:

Prime Factorisation
Long Division method
Listing common factors

Finding the HCF of 12 and 15 through Prime Factorisation

Prime Factorisation involves expressing numbers as the product of prime numbers. For instance, 12 and 15 can be expressed as;

12 = 2 × 2 × 3

15 = 3 × 5

The common Prime Factor is 3, so the HCF is,

HCF (12, 15) = 3.

Calculating the HCF of 12 and 15 using the Long Division Method

The Long division method involves several steps:

The smallest number from the set becomes the Divisor, and the larger number becomes the Dividend.
The smaller number then becomes the Dividend, and the remainder becomes the Divisor.
Repeat the above step until the remainder is zero.
The final Divisor is the HCF.

Using this method, the HCF of 12 and 15 is;

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Therefore, HCF (12, 15) = 3

Identifying the HCF of 12 and 15 by Listing the Factors

By listing all the factors of the given numbers, we can find the Highest/Greatest/Biggest common factor, which is the HCF. The factors for 12 and 15 are:

Factors of 12: 1, 2, 3 , 4, 6, and 12

Factors of 15: 1, 3 , 5, and 15.

Therefore, HCF (12, 15) = 3

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