Highest Common Factor of 7274, 2707 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 7274, 2707 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7274, 2707 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 7274, 2707 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 7274, 2707 is 1.

HCF(7274, 2707) = 1

HCF of 7274, 2707 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 7274, 2707 is 1.

Highest Common Factor of 7274,2707 using Euclid's algorithm

Highest Common Factor of 7274,2707 is 1

Step 1: Since 7274 > 2707, we apply the division lemma to 7274 and 2707, to get

7274 = 2707 x 2 + 1860

Step 2: Since the reminder 2707 ≠ 0, we apply division lemma to 1860 and 2707, to get

2707 = 1860 x 1 + 847

Step 3: We consider the new divisor 1860 and the new remainder 847, and apply the division lemma to get

1860 = 847 x 2 + 166

We consider the new divisor 847 and the new remainder 166,and apply the division lemma to get

847 = 166 x 5 + 17

We consider the new divisor 166 and the new remainder 17,and apply the division lemma to get

166 = 17 x 9 + 13

We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get

17 = 13 x 1 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 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 7274 and 2707 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(166,17) = HCF(847,166) = HCF(1860,847) = HCF(2707,1860) = HCF(7274,2707) .

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Frequently Asked Questions on HCF of 7274, 2707 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 7274, 2707?

Answer: HCF of 7274, 2707 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7274, 2707 using Euclid's Algorithm?

Answer: For arbitrary numbers 7274, 2707 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.