Highest Common Factor of 7586, 9661 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 7586, 9661 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7586, 9661 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 7586, 9661 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 7586, 9661 is 1.

HCF(7586, 9661) = 1

HCF of 7586, 9661 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 7586, 9661 is 1.

Highest Common Factor of 7586,9661 using Euclid's algorithm

Highest Common Factor of 7586,9661 is 1

Step 1: Since 9661 > 7586, we apply the division lemma to 9661 and 7586, to get

9661 = 7586 x 1 + 2075

Step 2: Since the reminder 7586 ≠ 0, we apply division lemma to 2075 and 7586, to get

7586 = 2075 x 3 + 1361

Step 3: We consider the new divisor 2075 and the new remainder 1361, and apply the division lemma to get

2075 = 1361 x 1 + 714

We consider the new divisor 1361 and the new remainder 714,and apply the division lemma to get

1361 = 714 x 1 + 647

We consider the new divisor 714 and the new remainder 647,and apply the division lemma to get

714 = 647 x 1 + 67

We consider the new divisor 647 and the new remainder 67,and apply the division lemma to get

647 = 67 x 9 + 44

We consider the new divisor 67 and the new remainder 44,and apply the division lemma to get

67 = 44 x 1 + 23

We consider the new divisor 44 and the new remainder 23,and apply the division lemma to get

44 = 23 x 1 + 21

We consider the new divisor 23 and the new remainder 21,and apply the division lemma to get

23 = 21 x 1 + 2

We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get

21 = 2 x 10 + 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 7586 and 9661 is 1

Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(44,23) = HCF(67,44) = HCF(647,67) = HCF(714,647) = HCF(1361,714) = HCF(2075,1361) = HCF(7586,2075) = HCF(9661,7586) .

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Frequently Asked Questions on HCF of 7586, 9661 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 7586, 9661?

Answer: HCF of 7586, 9661 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7586, 9661 using Euclid's Algorithm?

Answer: For arbitrary numbers 7586, 9661 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.