Highest Common Factor of 688, 17731 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 688, 17731 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 688, 17731 is 1 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 688, 17731 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 688, 17731 is 1.

HCF(688, 17731) = 1

HCF of 688, 17731 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 688, 17731 is 1.

Highest Common Factor of 688,17731 using Euclid's algorithm

Highest Common Factor of 688,17731 is 1

Step 1: Since 17731 > 688, we apply the division lemma to 17731 and 688, to get

17731 = 688 x 25 + 531

Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 531 and 688, to get

688 = 531 x 1 + 157

Step 3: We consider the new divisor 531 and the new remainder 157, and apply the division lemma to get

531 = 157 x 3 + 60

We consider the new divisor 157 and the new remainder 60,and apply the division lemma to get

157 = 60 x 2 + 37

We consider the new divisor 60 and the new remainder 37,and apply the division lemma to get

60 = 37 x 1 + 23

We consider the new divisor 37 and the new remainder 23,and apply the division lemma to get

37 = 23 x 1 + 14

We consider the new divisor 23 and the new remainder 14,and apply the division lemma to get

23 = 14 x 1 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 688 and 17731 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(23,14) = HCF(37,23) = HCF(60,37) = HCF(157,60) = HCF(531,157) = HCF(688,531) = HCF(17731,688) .

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Frequently Asked Questions on HCF of 688, 17731 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 688, 17731?

Answer: HCF of 688, 17731 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 688, 17731 using Euclid's Algorithm?

Answer: For arbitrary numbers 688, 17731 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.