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HCF of 56 and 70

HCF of 56 and 70 is the largest possible number that divides 56 and 70 exactly without any remainder. The factors of 56 and 70 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There are 3 commonly used methods to find the HCF of 56 and 70 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 56 and 70
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 56 and 70?

Answer: HCF of 56 and 70 is 14.

Explanation:

The HCF of two non-zero integers, x(56) and y(70), is the highest positive integer m(14) that divides both x(56) and y(70) without any remainder.

Methods to Find HCF of 56 and 70

The methods to find the HCF of 56 and 70 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 56 and 70 by Long Division

HCF of 56 and 70 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 70 (larger number) by 56 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (56) by the remainder (14).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (14) is the HCF of 56 and 70.

HCF of 56 and 70 by Listing Common Factors

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, that are 1, 2, 14, and 7. Therefore, the highest common factor of 56 and 70 is 14.

HCF of 56 and 70 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 70 and Y = 56

HCF(70, 56) = HCF(56, 70 mod 56) = HCF(56, 14)
HCF(56, 14) = HCF(14, 56 mod 14) = HCF(14, 0)
HCF(14, 0) = 14 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 56 and 70 is 14.

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HCF of 56 and 70 Examples

Example 1: Find the HCF of 56 and 70, if their LCM is 280.

Solution:

∵ LCM × HCF = 56 × 70
⇒ HCF(56, 70) = (56 × 70)/280 = 14
Therefore, the highest common factor of 56 and 70 is 14.
Example 2: The product of two numbers is 3920. If their HCF is 14, what is their LCM?

Solution:

Given: HCF = 14 and product of numbers = 3920
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 3920/14
Therefore, the LCM is 280.
Example 3: For two numbers, HCF = 14 and LCM = 280. If one number is 70, find the other number.

Solution:

Given: HCF (z, 70) = 14 and LCM (z, 70) = 280
∵ HCF × LCM = 70 × (z)
⇒ z = (HCF × LCM)/70
⇒ z = (14 × 280)/70
⇒ z = 56
Therefore, the other number is 56.

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FAQs on HCF of 56 and 70

What is the HCF of 56 and 70?

The HCF of 56 and 70 is 14. To calculate the Highest common factor of 56 and 70, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and choose the highest factor that exactly divides both 56 and 70, i.e., 14.

How to Find the HCF of 56 and 70 by Prime Factorization?

To find the HCF of 56 and 70, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 70 = 2 × 5 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 56 and 70. Hence, HCF(56, 70) = 2 × 7 = 14
☛ Prime Number

What is the Relation Between LCM and HCF of 56, 70?

The following equation can be used to express the relation between LCM and HCF of 56 and 70, i.e. HCF × LCM = 56 × 70.

If the HCF of 70 and 56 is 14, Find its LCM.

HCF(70, 56) × LCM(70, 56) = 70 × 56
Since the HCF of 70 and 56 = 14
⇒ 14 × LCM(70, 56) = 3920
Therefore, LCM = 280
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What are the Methods to Find HCF of 56 and 70?

There are three commonly used methods to find the HCF of 56 and 70.

By Prime Factorization
By Listing Common Factors
By Long Division

How to Find the HCF of 56 and 70 by Long Division Method?

To find the HCF of 56, 70 using long division method, 70 is divided by 56. The corresponding divisor (14) when remainder equals 0 is taken as HCF.

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