Highest Common Factor of 9712, 7140 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 9712, 7140 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 9712, 7140 is 4 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 9712, 7140 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 9712, 7140 is 4.

HCF(9712, 7140) = 4

HCF of 9712, 7140 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 9712, 7140 is 4.

Highest Common Factor of 9712,7140 using Euclid's algorithm

Highest Common Factor of 9712,7140 is 4

Step 1: Since 9712 > 7140, we apply the division lemma to 9712 and 7140, to get

9712 = 7140 x 1 + 2572

Step 2: Since the reminder 7140 ≠ 0, we apply division lemma to 2572 and 7140, to get

7140 = 2572 x 2 + 1996

Step 3: We consider the new divisor 2572 and the new remainder 1996, and apply the division lemma to get

2572 = 1996 x 1 + 576

We consider the new divisor 1996 and the new remainder 576,and apply the division lemma to get

1996 = 576 x 3 + 268

We consider the new divisor 576 and the new remainder 268,and apply the division lemma to get

576 = 268 x 2 + 40

We consider the new divisor 268 and the new remainder 40,and apply the division lemma to get

268 = 40 x 6 + 28

We consider the new divisor 40 and the new remainder 28,and apply the division lemma to get

40 = 28 x 1 + 12

We consider the new divisor 28 and the new remainder 12,and apply the division lemma to get

28 = 12 x 2 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 9712 and 7140 is 4

Notice that 4 = HCF(12,4) = HCF(28,12) = HCF(40,28) = HCF(268,40) = HCF(576,268) = HCF(1996,576) = HCF(2572,1996) = HCF(7140,2572) = HCF(9712,7140) .

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Frequently Asked Questions on HCF of 9712, 7140 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 9712, 7140?

Answer: HCF of 9712, 7140 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9712, 7140 using Euclid's Algorithm?

Answer: For arbitrary numbers 9712, 7140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.