Highest Common Factor of 665, 875, 656 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 665, 875, 656 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 665, 875, 656 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 665, 875, 656 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 665, 875, 656 is 1.

HCF(665, 875, 656) = 1

HCF of 665, 875, 656 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 665, 875, 656 is 1.

Highest Common Factor of 665,875,656 using Euclid's algorithm

Highest Common Factor of 665,875,656 is 1

Step 1: Since 875 > 665, we apply the division lemma to 875 and 665, to get

875 = 665 x 1 + 210

Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 210 and 665, to get

665 = 210 x 3 + 35

Step 3: We consider the new divisor 210 and the new remainder 35, and apply the division lemma to get

210 = 35 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 665 and 875 is 35

Notice that 35 = HCF(210,35) = HCF(665,210) = HCF(875,665) .

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

Step 1: Since 656 > 35, we apply the division lemma to 656 and 35, to get

656 = 35 x 18 + 26

Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 26 and 35, to get

35 = 26 x 1 + 9

Step 3: We consider the new divisor 26 and the new remainder 9, and apply the division lemma to get

26 = 9 x 2 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 35 and 656 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(26,9) = HCF(35,26) = HCF(656,35) .

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Frequently Asked Questions on HCF of 665, 875, 656 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 665, 875, 656?

Answer: HCF of 665, 875, 656 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 665, 875, 656 using Euclid's Algorithm?

Answer: For arbitrary numbers 665, 875, 656 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.