The HCF of 56 and 70 is 14. The greatest number that divides 56 and 70 perfectly without leaving a residual is the HCF of these numbers. The factors for the numbers 56 and 70 are 1, 2, 4, 7, 8, 14, 56 and 1, 2, 5, 7, 10, 14, 35, and 70, respectively. Listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 56 and 70.
Also read: Highest common factor
What is the HCF of 56 and 70?
The answer to this question is 14. This article shows the HCF of 56 and 70 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 56 and 70?
There are three methods to find the HCF of 56 and 70:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 56 and 70 by Prime Factorisation Method
The prime factorisation of 56 and 70 is given by:
Prime factorisation of 56 = (2 × 2 × 2 × 7)
Prime factorisation of 70 = (2 × 5 × 7)
The common prime factors of 56 and 70 are 2 and 7.
Hence, the HCF of 56 and 70 = 2 x 7 = 14.
HCF (56, 70) = 14
HCF of 56 and 70 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing a long division repeatedly is HCF of 56 and 70.
No further division can be done.
Hence, HCF (56, 70) = 14
HCF of 56 and 70 by Listing Common Factors
To calculate the HCF of 56 and 70 by listing out the common factors, list the factors as shown below:
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
There are 4 common factors of 56 and 70, and they are 1, 2, 7, and 14. Therefore, the highest common factor of 56 and 70 is 14.
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HCF of 56 and 70 Solved Example
Find the HCF of 56 and 70, if their LCM is 280.
Solution:
Given
LCM × HCF = 56 × 70
⇒ HCF(56, 70) = (56 × 70)/280 = 14
HCF(56, 70) = 3920/280 = 14
Therefore, the highest common factor of 56 and 70 is 14.
Frequently Asked Questions on HCF of 56 and 70
What is the HCF of 56 and 70?
How to find the HCF of 56 and 70 by Prime Factorisation?
⇒ Since 2 and 7 are common numbers in the prime factorisation of 56 and 70, HCF(56, 70) = 2 × 7 = 14.
What is the relation between LCM and HCF of 56, 70?
If the HCF of 70 and 56 is 14, find its LCM.
Since the HCF of 70 and 56 = 14
⇒ 14 × LCM(70, 56) = 3920
Therefore, LCM = 3920/14 = 280
What are the methods to find the HCF of 56 and 70?
By Long Division
By Listing Common Factors
By Prime Factorisation
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