Highest Common Factor of 977, 708 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 977, 708 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 977, 708 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 977, 708 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 977, 708 is 1.

HCF(977, 708) = 1

HCF of 977, 708 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 977, 708 is 1.

Highest Common Factor of 977,708 using Euclid's algorithm

Highest Common Factor of 977,708 is 1

Step 1: Since 977 > 708, we apply the division lemma to 977 and 708, to get

977 = 708 x 1 + 269

Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 269 and 708, to get

708 = 269 x 2 + 170

Step 3: We consider the new divisor 269 and the new remainder 170, and apply the division lemma to get

269 = 170 x 1 + 99

We consider the new divisor 170 and the new remainder 99,and apply the division lemma to get

170 = 99 x 1 + 71

We consider the new divisor 99 and the new remainder 71,and apply the division lemma to get

99 = 71 x 1 + 28

We consider the new divisor 71 and the new remainder 28,and apply the division lemma to get

71 = 28 x 2 + 15

We consider the new divisor 28 and the new remainder 15,and apply the division lemma to get

28 = 15 x 1 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 977 and 708 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(71,28) = HCF(99,71) = HCF(170,99) = HCF(269,170) = HCF(708,269) = HCF(977,708) .

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Frequently Asked Questions on HCF of 977, 708 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 977, 708?

Answer: HCF of 977, 708 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 977, 708 using Euclid's Algorithm?

Answer: For arbitrary numbers 977, 708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.