Highest Common Factor of 7148, 9880 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 7148, 9880 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 7148, 9880 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 7148, 9880 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 7148, 9880 is 4.

HCF(7148, 9880) = 4

HCF of 7148, 9880 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 7148, 9880 is 4.

Highest Common Factor of 7148,9880 using Euclid's algorithm

Highest Common Factor of 7148,9880 is 4

Step 1: Since 9880 > 7148, we apply the division lemma to 9880 and 7148, to get

9880 = 7148 x 1 + 2732

Step 2: Since the reminder 7148 ≠ 0, we apply division lemma to 2732 and 7148, to get

7148 = 2732 x 2 + 1684

Step 3: We consider the new divisor 2732 and the new remainder 1684, and apply the division lemma to get

2732 = 1684 x 1 + 1048

We consider the new divisor 1684 and the new remainder 1048,and apply the division lemma to get

1684 = 1048 x 1 + 636

We consider the new divisor 1048 and the new remainder 636,and apply the division lemma to get

1048 = 636 x 1 + 412

We consider the new divisor 636 and the new remainder 412,and apply the division lemma to get

636 = 412 x 1 + 224

We consider the new divisor 412 and the new remainder 224,and apply the division lemma to get

412 = 224 x 1 + 188

We consider the new divisor 224 and the new remainder 188,and apply the division lemma to get

224 = 188 x 1 + 36

We consider the new divisor 188 and the new remainder 36,and apply the division lemma to get

188 = 36 x 5 + 8

We consider the new divisor 36 and the new remainder 8,and apply the division lemma to get

36 = 8 x 4 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 7148 and 9880 is 4

Notice that 4 = HCF(8,4) = HCF(36,8) = HCF(188,36) = HCF(224,188) = HCF(412,224) = HCF(636,412) = HCF(1048,636) = HCF(1684,1048) = HCF(2732,1684) = HCF(7148,2732) = HCF(9880,7148) .

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Frequently Asked Questions on HCF of 7148, 9880 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 7148, 9880?

Answer: HCF of 7148, 9880 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7148, 9880 using Euclid's Algorithm?

Answer: For arbitrary numbers 7148, 9880 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.