HCF of 36 and 48

The HCF of 36 and 48 is 12. The listing common factors, long division, and prime factorisation are the three most important methods for calculating the HCF of 36 and 48. The greatest possible number that divides 36 and 48 perfectly without any remainder is the HCF of 36 and 48. The factors of 36 and 48 are 1, 2, 3, 4, 6, 8, 12, 16, and 24 and 1, 2, 3, 4, 6, 9, 12, 18, 36, respectively.

Also read: Highest common factor

What is the HCF of 36 and 48?

The answer to this question is 12. This article shows the HCF of 36 and 48 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 36 and 48?

There are three methods to find the HCF of 36 and 48:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 36 and 48 by Prime Factorisation Method

The prime factorisation of 36 and 48 is given by:

Prime factorisation of 36 = (2 × 2 × 3 × 3)

Prime factorisation of 48 = (2 × 2 × 2 × 2 × 3)

Hence, the HCF of 36 and 48 is 2 × 2 × 3 = 12.

HCF (36, 48) = 12

HCF of 36 and 48 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 36 and 48.

HCF of 36 and 48

No further division can be done. 

Hence, HCF (36, 48) = 12

HCF of 36 and 48 by Listing the Factors

To calculate the HCF of 36 and 48 by listing out the common factors, list the factors as shown below:

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

There are 6 common factors of 36 and 48, i.e. 1, 2, 3, 4, 6 and 12. Therefore, the highest common factor of 36 and 48 is 12.

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Video Lesson on Properties of HCF and LCM

HCF of 36 and 48 Solved Example

The product of two numbers is 1728. If their HCF is 12, what is their LCM?

Solution:

Given: HCF = 12 and product of numbers = 1728

LCM × HCF = product of numbers

⇒ LCM = Product/HCF = 1728/12

Therefore, the LCM is 144.

Frequently Asked Questions on HCF of 36 and 48

Q1

What is the HCF of 36 and 48?

The HCF of 36 and 48 is 12. To calculate the HCF (Highest Common Factor) of 36 and 48, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the highest factor that exactly divides both 36 and 48, i.e. 12.
Q2

How to find the HCF of 36 and 48 by Long Division Method?

To find the HCF of 36, 48 using the long division method, 48 is divided by 36. The corresponding divisor (12) when remainder equals 0 is taken as HCF.
Q3

How to find the HCF of 36 and 48 by prime factorisation?

To find the HCF of 36 and 48, we will find the prime factorisation of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 3 are common numbers in the prime factorisation of 36 and 48, HCF(36, 48) = 2 × 2 × 3 = 12

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