Highest Common Factor of 688, 781, 64 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, 781, 64 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 688, 781, 64 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, 781, 64 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, 781, 64 is 1.

HCF(688, 781, 64) = 1

HCF of 688, 781, 64 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, 781, 64 is 1.

Highest Common Factor of 688,781,64 using Euclid's algorithm

Highest Common Factor of 688,781,64 is 1

Step 1: Since 781 > 688, we apply the division lemma to 781 and 688, to get

781 = 688 x 1 + 93

Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 93 and 688, to get

688 = 93 x 7 + 37

Step 3: We consider the new divisor 93 and the new remainder 37, and apply the division lemma to get

93 = 37 x 2 + 19

We consider the new divisor 37 and the new remainder 19,and apply the division lemma to get

37 = 19 x 1 + 18

We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get

19 = 18 x 1 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 688 and 781 is 1

Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(93,37) = HCF(688,93) = HCF(781,688) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 64 > 1, we apply the division lemma to 64 and 1, to get

64 = 1 x 64 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 64 is 1

Notice that 1 = HCF(64,1) .

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Frequently Asked Questions on HCF of 688, 781, 64 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, 781, 64?

Answer: HCF of 688, 781, 64 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 688, 781, 64 using Euclid's Algorithm?

Answer: For arbitrary numbers 688, 781, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.