# Highest Common Factor of 560, 706 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 560, 706 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 706 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 560, 706 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 560, 706 is 2.

HCF(560, 706) = 2

## HCF of 560, 706 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 560, 706 is 2. ### Highest Common Factor of 560,706 is 2

Step 1: Since 706 > 560, we apply the division lemma to 706 and 560, to get

706 = 560 x 1 + 146

Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 146 and 560, to get

560 = 146 x 3 + 122

Step 3: We consider the new divisor 146 and the new remainder 122, and apply the division lemma to get

146 = 122 x 1 + 24

We consider the new divisor 122 and the new remainder 24,and apply the division lemma to get

122 = 24 x 5 + 2

We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get

24 = 2 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 560 and 706 is 2

Notice that 2 = HCF(24,2) = HCF(122,24) = HCF(146,122) = HCF(560,146) = HCF(706,560) .

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### Frequently Asked Questions on HCF of 560, 706 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 560, 706?

Answer: HCF of 560, 706 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 706 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.