HCF of 294 252 and 210

The HCF of 294, 252 and 210 is 42. HCF of 294, 252 and 210 is the largest possible number that divides 294, 252 and 210 exactly without any remainder. The factors of 294, 252 and 210 are:

294: 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294

252: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 294, 252 and 210. 

Also read: Highest common factor

What is the HCF of 294, 252 and 210?

The answer to this question is 42. This article shows the HCF of 294, 252 and 210 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 294, 252 and 210?

There are three methods to find the HCF of 294, 252 and 210:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 294, 252 and 210 by Prime Factorisation Method

The prime factorisation of 294, 252 and 210 is given by:

Prime factorisation of 294 = (2 × 3 × 7 × 7)

Prime factorisation of 252 = (2 × 2 × 3 × 3 × 7)

Prime factorisation of 210 = (2 × 3 × 5 × 7) 

Hence, the HCF of 294, 252 and 210 is 2 × 3 × 7 = 42.

HCF (294, 252, 210) = 42

HCF of 294, 252 and 210 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 294, 252 and 210.

HCF of 294 252 and 210 1 HCF of 294 252 and 210 2 HCF of 294 252 and 210 3

No further division can be done. 

Hence, HCF (294, 252, 210) = 42

HCF of 294, 252 and 210 by Listing the Factors

To calculate the HCF of 294, 252 and 210 by listing out the common factors, list the factors as shown below:

Factors of number 294: 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294

Factors of number 252: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

Factors of number 210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

There are 8 common factors of 294, 252 and 210, that are 1, 2, 3, 6, 7, 14, 21, and 42. Therefore, the highest common factor of 294, 252 and 210 is 42.

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HCF of 294, 252 and 210 Solved Example

Find the highest number that divides 294, 252, and 210 completely.

Solution:

The highest number that divides 294, 252, and 210 exactly is their highest common factor.

Factors of 294 = 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294

Factors of 252 = 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

Factors of 210 = 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

The HCF of 294, 252, and 210 is 42.

The highest number that divides 294, 252, and 210 is 42.

Frequently Asked Questions on HCF of 294, 252 and 210

Q1

What is the HCF of 294, 252 and 210?

The HCF of 294, 252 and 210 is 42. To calculate the highest common factor of 294, 252 and 210, we need to factor each number and choose the highest factor that exactly divides 294, 252 and 210, i.e., 42.
Q2

How to Find the HCF of 294, 252 and 210 by Prime Factorisation?

To find the HCF of 294, 252 and 210, we will find the prime factorization of given numbers, i.e. 294 = 2 × 3 × 7 × 7; 252 = 2 × 2 × 3 × 3 × 7; 210 = 2 × 3 × 5 × 7. ⇒ Since 2, 3, 7 are common terms in the prime factorization of 294, 252 and 210. Hence, HCF(294, 252, 210) = 2 × 3 × 7 = 42
Q3

What are the Methods to Find HCF of 294, 252 and 210?

There are three commonly used methods to find the HCF of 294, 252 and 210. By Long Division By Listing Common Factors By Prime Factorisation
Q4

Which of the following is HCF of 294, 252 and 210? 42, 307, 46, 48, 66

HCF of 294, 252, 210 will be the number that divides 294, 252, and 210 without leaving any remainder. The only number that satisfies the given condition is 42.
Q5

What is the Relation Between LCM and HCF of 294, 252 and 210?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 294, 252 and 210, i.e. HCF(294, 252, 210) = [(294 × 252 × 210) × LCM(294, 252, 210)]/[LCM(294, 252) × LCM (252, 210) × LCM(294, 210)].

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