HCF of 8 10 and 12

The HCF of 8, 10 and 12 is 2. The greatest number that divides 8, 10, and 12 perfectly, leaving no remainder, is known as the HCF of 8, 10, and 12. Factors of 8, 10, and 12 are, respectively, (1, 2, 4, 8), (1, 2, 5, 10), and (1, 2, 3, 4, 6, 12). The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 8, 10 and 12.

Also read: Highest common factor

What is the HCF of 8, 10 and 12?

The answer to this question is 2. This article shows the HCF of 8, 10 and 12 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 8, 10 and 12?

There are three methods to find the HCF of 8, 10 and 12:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 8, 10 and 12 by Prime Factorisation Method

The prime factorisation of 8, 10 and 12 is given by:

Prime factorisation of 8 = (2 × 2 × 2)

Prime factorisation of 10 = (2 × 5)

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

Hence, the HCF of 8, 10 and 12 is 2.

HCF (8, 10, 12) = 2

HCF of 8, 10 and 12 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 8, 10 and 12.

HCF of 8 10 and 12 1 HCF of 8 10 and 12 2 HCF of 8 10 and 12 3

No further division can be done. 

Hence, HCF (8, 10, 12) = 2

HCF of 8, 10 and 12 by Listing the Factors

To calculate the HCF of 8, 10 and 12 by listing out the common factors, list the factors as shown below:

Factors of 8: 1, 2, 4, 8

Factors of 10: 1, 2, 5, 10

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

There are 2 common factors of 8, 10 and 12, that are 1 and 2. Therefore, the highest common factor of 8, 10 and 12 is 2.

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Video Lesson on Properties of HCF and LCM

HCF of 8, 10 and 12 Solved Example

Find the highest number that divides 8, 10, and 12 completely.

Solution:

The highest number that divides 8, 10, and 12 exactly is their highest common factor.

Factors of 8 = 1, 2, 4, 8

Factors of 10 = 1, 2, 5, 10

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

The HCF of 8, 10, and 12 is 2.

The highest number that divides 8, 10, and 12 is 2.

Frequently Asked Questions on HCF of 8, 10 and 12

Q1

What is the HCF of 8, 10 and 12?

The HCF of 8, 10 and 12 is 2. To calculate the HCF of 8, 10 and 12, we need to factor each number and choose the highest factor that exactly divides 8, 10 and 12, i.e., 2.
Q2

How to Find the HCF of 8, 10 and 12 by Prime Factorisation?

To find the HCF of 8, 10 and 12, we will find the prime factorization of given numbers, i.e. 8 = 2 × 2 × 2; 10 = 2 × 5; 12 = 2 × 2 × 3. ⇒ Since 2 is the only common prime factor of 8, 10 and 12. Hence, HCF(8, 10, 12) = 2.
Q3

What are the Methods to Find HCF of 8, 10 and 12?

There are three commonly used methods to find the HCF of 8, 10 and 12. By Long Division By Listing Common Factors By Prime Factorisation
Q4

Which of the following is HCF of 8, 10 and 12? 2, 31, 46, 56, 17

HCF of 8, 10, 12 will be the number that divides 8, 10, and 12 without leaving any remainder. The only number that satisfies the given condition is 2.
Q5

What is the Relation Between LCM and HCF of 8, 10 and 12?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 8, 10 and 12, i.e. HCF(8, 10, 12) = [(8 × 10 × 12) × LCM(8, 10, 12)]/[LCM(8, 10) × LCM (10, 12) × LCM(8, 12)].

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