Highest Common Factor of 688, 864, 781 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, 864, 781 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 688, 864, 781 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, 864, 781 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, 864, 781 is 1.

HCF(688, 864, 781) = 1

HCF of 688, 864, 781 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, 864, 781 is 1.

Highest Common Factor of 688,864,781 using Euclid's algorithm

Highest Common Factor of 688,864,781 is 1

Step 1: Since 864 > 688, we apply the division lemma to 864 and 688, to get

864 = 688 x 1 + 176

Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 176 and 688, to get

688 = 176 x 3 + 160

Step 3: We consider the new divisor 176 and the new remainder 160, and apply the division lemma to get

176 = 160 x 1 + 16

We consider the new divisor 160 and the new remainder 16, and apply the division lemma to get

160 = 16 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 688 and 864 is 16

Notice that 16 = HCF(160,16) = HCF(176,160) = HCF(688,176) = HCF(864,688) .

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

Step 1: Since 781 > 16, we apply the division lemma to 781 and 16, to get

781 = 16 x 48 + 13

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 13 and 16, to get

16 = 13 x 1 + 3

Step 3: We consider the new divisor 13 and the new remainder 3, and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 16 and 781 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(781,16) .

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Frequently Asked Questions on HCF of 688, 864, 781 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, 864, 781?

Answer: HCF of 688, 864, 781 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 688, 864, 781 using Euclid's Algorithm?

Answer: For arbitrary numbers 688, 864, 781 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.