HCF of 12 16 and 24

The HCF of 12, 16 and 24 is 4. The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 12, 16 and 24. The greatest number that divides 12, 16, and 24 perfectly without leaving a remainder is called the HCF of 12, 16, and 24. The set of numbers “(1, 2, 3, 4, 6, 12), (1, 2, 4, 8, 16), and (1, 2, 3, 4, 6, 8, 12, 24)”, respectively, that make up the factors of 12, 16, and 24.

Also read: Highest common factor

What is the HCF of 12, 16 and 24?

The answer to this question is 4. This article shows the HCF of 12, 16 and 24 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 12, 16 and 24?

There are three methods to find the HCF of 12, 16 and 24:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 12, 16 and 24 by Prime Factorisation Method

The prime factorisation of 12, 16 and 24 is given by:

Prime factorisation of 12 = (2 × 2 × 3)

Prime factorisation of 16 = (2 × 2 × 2 × 2)

Prime factorisation of 24 = (2 × 2 × 2 × 3)

Hence, the HCF of 12, 16 and 24 is 4.

HCF (12, 16, 24) = 4

HCF of 12, 16 and 24 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 12, 16 and 24.

HCF of 12, 16 and 24

HCF of 12, 16 and 24

No further division can be done.

Hence, HCF (12, 16, 24) = 4

HCF of 12, 16 and 24 by Listing the Factors

To calculate the HCF of 12, 16 and 24 by listing out the common factors, list the factors as shown below:

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

Factors of 16: 1, 2, 4, 8, 16

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

There are 3 common factors of 12, 16 and 24, that are 1, 2, and 4. Therefore, the highest common factor of 12, 16 and 24 is 4.

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HCF of 12, 16 and 24 Solved Example

Find the highest number that divides 12, 16, and 24 completely.

Solution:

The highest number that divides 12, 16, and 24 exactly is their highest common factor.

Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 16 = 1, 2, 4, 8, 16

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

The HCF of 12, 16, and 24 is 4.

The highest number that divides 12, 16, and 24 is 4.

Frequently Asked Questions on HCF of 12, 16 and 24

Q1

What is the HCF of 12, 16 and 24?

The HCF of 12, 16 and 24 is 4. To calculate the HCF (Highest Common Factor) of 12, 16 and 24, we need to factor each number and choose the highest factor that exactly divides 12, 16 and 24, i.e., 4.
Q2

How to Find the HCF of 12, 16 and 24 by Prime Factorisation?

To find the HCF of 12, 16 and 24, we will find the prime factorization of given numbers, i.e. 12 = 2 × 2 × 3; 16 = 2 × 2 × 2 × 2; 24 = 2 × 2 × 2 × 3. ⇒ Since 2, 2 are common terms in the prime factorization of 12, 16 and 24. Hence, HCF(12, 16, 24) = 2 × 2 = 4
Q3

What are the Methods to Find HCF of 12, 16 and 24?

There are three commonly used methods to find the HCF of 12, 16 and 24. By Long Division By Listing Common Factors By Prime Factorisation
Q4

Which of the following is HCF of 12, 16 and 24? 4, 25, 51, 63, 62, 66, 64, 39

HCF of 12, 16, 24 will be the number that divides 12, 16, and 24 without leaving any remainder. The only number that satisfies the given condition is 4.
Q5

What is the Relation Between LCM and HCF of 12, 16 and 24?

The following equation can be used to express the relation between LCM and HCF of 12, 16 and 24, i.e. HCF(12, 16, 24) = [(12 × 16 × 24) × LCM(12, 16, 24)]/[LCM(12, 16) × LCM (16, 24) × LCM(12, 24)].

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