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.
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.
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