Highest Common Factor of 2688, 7561 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 2688, 7561 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2688, 7561 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 2688, 7561 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 2688, 7561 is 1.

HCF(2688, 7561) = 1

HCF of 2688, 7561 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 2688, 7561 is 1.

Highest Common Factor of 2688,7561 using Euclid's algorithm

Highest Common Factor of 2688,7561 is 1

Step 1: Since 7561 > 2688, we apply the division lemma to 7561 and 2688, to get

7561 = 2688 x 2 + 2185

Step 2: Since the reminder 2688 ≠ 0, we apply division lemma to 2185 and 2688, to get

2688 = 2185 x 1 + 503

Step 3: We consider the new divisor 2185 and the new remainder 503, and apply the division lemma to get

2185 = 503 x 4 + 173

We consider the new divisor 503 and the new remainder 173,and apply the division lemma to get

503 = 173 x 2 + 157

We consider the new divisor 173 and the new remainder 157,and apply the division lemma to get

173 = 157 x 1 + 16

We consider the new divisor 157 and the new remainder 16,and apply the division lemma to get

157 = 16 x 9 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2688 and 7561 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(157,16) = HCF(173,157) = HCF(503,173) = HCF(2185,503) = HCF(2688,2185) = HCF(7561,2688) .

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Frequently Asked Questions on HCF of 2688, 7561 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 2688, 7561?

Answer: HCF of 2688, 7561 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2688, 7561 using Euclid's Algorithm?

Answer: For arbitrary numbers 2688, 7561 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.