HCF of 24 and 36

Created by: Team Maths - Examples.com, Last Updated: May 27, 2024

HCF of 24 and 36

The Highest Common Factor (HCF) of 24 and 36 is 12. The HCF, also known as the Greatest Common Factor (GCF), is the largest number that can divide both 24 and 36 without leaving a remainder. The common factors of 24 and 36 are 1, 2, 3, 4, 6, and 12, with 12 being the highest. There are three common methods to find the HCF: prime factorization, Euclidean algorithm, and long division. In this case, the HCF of 24 and 36 is determined to be 12, as it is the largest number that can perfectly divide both numbers.

What is HCF of 24 and 36?

HCF of 24 and 36 is 12

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, while the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The Highest Common Factor (HCF) of two non-zero integers, 24 and 36, is the largest positive integer, 12, that can divide both 24 and 36 without leaving a remainder.

Methods to Find HCF of 24 and 36

1. Prime Factorization Method
2. Long Division Method
3. Listing Common Factors

HCF of 24 and 36 by Prime Factorization

The prime factorization of 24 is 2×2×2×3 and for 36, it is 2×2×3×3. Both 24 and 36 share common prime factors. Therefore, the Highest Common Factor (HCF) of 24 and 36 is 2×2×3=12.

HCF of 24 and 36 by Long Division

1. Divide the larger number by the smaller number:
• Divide 36 by 24.The quotient is 1 and the remainder is 12.
36÷24=1 remainder 12
2. Replace the larger number with the smaller number, and the smaller number with the remainder:
• Now, divide 24 (the previous divisor) by 12 (the remainder from step 1).The quotient is 2 and the remainder is 0.
24÷12=2 remainder 0
3. Continue the process until the remainder is 0:
• When the remainder becomes 0, the divisor at this stage (12) is the HCF.
Since the remainder is now 0, the HCF of 24 and 36 is 12.

HCF of 24 and 36 by Listing Common Factors

There are six common factors of 24 and 36: 1, 2, 3, 4, 6, and 12. Therefore, the Highest Common Factor (HCF) of 24 and 36 is 12.

How do you find the HCF of 24 and 36?

The HCF of 24 and 36 can be found using prime factorization, the Euclidean algorithm, or the long division method.

What are the common factors of 24 and 36?

The common factors of 24 and 36 are 1, 2, 3, 4, 6, and 12.

Why is the HCF of 24 and 36 important?

The HCF helps simplify fractions and solve problems involving ratios and common divisors.

Can the HCF of 24 and 36 be greater than 12?

No, the HCF is the greatest common factor. For 24 and 36, it is 12.

What is the smallest common factor of 24 and 36?

The smallest common factor of 24 and 36 is 1.

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