Highest Common Factor of 687, 402, 564 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 687, 402, 564 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 687, 402, 564 is 3 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 687, 402, 564 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 687, 402, 564 is 3.

HCF(687, 402, 564) = 3

HCF of 687, 402, 564 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 687, 402, 564 is 3.

Highest Common Factor of 687,402,564 using Euclid's algorithm

Highest Common Factor of 687,402,564 is 3

Step 1: Since 687 > 402, we apply the division lemma to 687 and 402, to get

687 = 402 x 1 + 285

Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 285 and 402, to get

402 = 285 x 1 + 117

Step 3: We consider the new divisor 285 and the new remainder 117, and apply the division lemma to get

285 = 117 x 2 + 51

We consider the new divisor 117 and the new remainder 51,and apply the division lemma to get

117 = 51 x 2 + 15

We consider the new divisor 51 and the new remainder 15,and apply the division lemma to get

51 = 15 x 3 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 687 and 402 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(51,15) = HCF(117,51) = HCF(285,117) = HCF(402,285) = HCF(687,402) .

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

Step 1: Since 564 > 3, we apply the division lemma to 564 and 3, to get

564 = 3 x 188 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 564 is 3

Notice that 3 = HCF(564,3) .

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Frequently Asked Questions on HCF of 687, 402, 564 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 687, 402, 564?

Answer: HCF of 687, 402, 564 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 687, 402, 564 using Euclid's Algorithm?

Answer: For arbitrary numbers 687, 402, 564 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.