Highest Common Factor of 971, 707, 102 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 971, 707, 102 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 971, 707, 102 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 971, 707, 102 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 971, 707, 102 is 1.

HCF(971, 707, 102) = 1

HCF of 971, 707, 102 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 971, 707, 102 is 1.

Highest Common Factor of 971,707,102 using Euclid's algorithm

Highest Common Factor of 971,707,102 is 1

Step 1: Since 971 > 707, we apply the division lemma to 971 and 707, to get

971 = 707 x 1 + 264

Step 2: Since the reminder 707 ≠ 0, we apply division lemma to 264 and 707, to get

707 = 264 x 2 + 179

Step 3: We consider the new divisor 264 and the new remainder 179, and apply the division lemma to get

264 = 179 x 1 + 85

We consider the new divisor 179 and the new remainder 85,and apply the division lemma to get

179 = 85 x 2 + 9

We consider the new divisor 85 and the new remainder 9,and apply the division lemma to get

85 = 9 x 9 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 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 971 and 707 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(85,9) = HCF(179,85) = HCF(264,179) = HCF(707,264) = HCF(971,707) .

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

Step 1: Since 102 > 1, we apply the division lemma to 102 and 1, to get

102 = 1 x 102 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 102 is 1

Notice that 1 = HCF(102,1) .

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Frequently Asked Questions on HCF of 971, 707, 102 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 971, 707, 102?

Answer: HCF of 971, 707, 102 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 971, 707, 102 using Euclid's Algorithm?

Answer: For arbitrary numbers 971, 707, 102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.