Highest Common Factor of 608, 977, 715 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 608, 977, 715 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 608, 977, 715 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 608, 977, 715 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 608, 977, 715 is 1.

HCF(608, 977, 715) = 1

HCF of 608, 977, 715 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 608, 977, 715 is 1.

Highest Common Factor of 608,977,715 using Euclid's algorithm

Highest Common Factor of 608,977,715 is 1

Step 1: Since 977 > 608, we apply the division lemma to 977 and 608, to get

977 = 608 x 1 + 369

Step 2: Since the reminder 608 ≠ 0, we apply division lemma to 369 and 608, to get

608 = 369 x 1 + 239

Step 3: We consider the new divisor 369 and the new remainder 239, and apply the division lemma to get

369 = 239 x 1 + 130

We consider the new divisor 239 and the new remainder 130,and apply the division lemma to get

239 = 130 x 1 + 109

We consider the new divisor 130 and the new remainder 109,and apply the division lemma to get

130 = 109 x 1 + 21

We consider the new divisor 109 and the new remainder 21,and apply the division lemma to get

109 = 21 x 5 + 4

We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get

21 = 4 x 5 + 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 608 and 977 is 1

Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(109,21) = HCF(130,109) = HCF(239,130) = HCF(369,239) = HCF(608,369) = HCF(977,608) .

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

Step 1: Since 715 > 1, we apply the division lemma to 715 and 1, to get

715 = 1 x 715 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 715 is 1

Notice that 1 = HCF(715,1) .

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Frequently Asked Questions on HCF of 608, 977, 715 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 608, 977, 715?

Answer: HCF of 608, 977, 715 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 608, 977, 715 using Euclid's Algorithm?

Answer: For arbitrary numbers 608, 977, 715 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.