Highest Common Factor of 9965, 7178 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 9965, 7178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9965, 7178 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 9965, 7178 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 9965, 7178 is 1.

HCF(9965, 7178) = 1

HCF of 9965, 7178 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 9965, 7178 is 1.

Highest Common Factor of 9965,7178 using Euclid's algorithm

Highest Common Factor of 9965,7178 is 1

Step 1: Since 9965 > 7178, we apply the division lemma to 9965 and 7178, to get

9965 = 7178 x 1 + 2787

Step 2: Since the reminder 7178 ≠ 0, we apply division lemma to 2787 and 7178, to get

7178 = 2787 x 2 + 1604

Step 3: We consider the new divisor 2787 and the new remainder 1604, and apply the division lemma to get

2787 = 1604 x 1 + 1183

We consider the new divisor 1604 and the new remainder 1183,and apply the division lemma to get

1604 = 1183 x 1 + 421

We consider the new divisor 1183 and the new remainder 421,and apply the division lemma to get

1183 = 421 x 2 + 341

We consider the new divisor 421 and the new remainder 341,and apply the division lemma to get

421 = 341 x 1 + 80

We consider the new divisor 341 and the new remainder 80,and apply the division lemma to get

341 = 80 x 4 + 21

We consider the new divisor 80 and the new remainder 21,and apply the division lemma to get

80 = 21 x 3 + 17

We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get

21 = 17 x 1 + 4

We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get

17 = 4 x 4 + 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 9965 and 7178 is 1

Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(80,21) = HCF(341,80) = HCF(421,341) = HCF(1183,421) = HCF(1604,1183) = HCF(2787,1604) = HCF(7178,2787) = HCF(9965,7178) .

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Frequently Asked Questions on HCF of 9965, 7178 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 9965, 7178?

Answer: HCF of 9965, 7178 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9965, 7178 using Euclid's Algorithm?

Answer: For arbitrary numbers 9965, 7178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.