Highest Common Factor of 735, 8629 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 735, 8629 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 735, 8629 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 735, 8629 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 735, 8629 is 1.

HCF(735, 8629) = 1

HCF of 735, 8629 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 735, 8629 is 1.

Highest Common Factor of 735,8629 using Euclid's algorithm

Highest Common Factor of 735,8629 is 1

Step 1: Since 8629 > 735, we apply the division lemma to 8629 and 735, to get

8629 = 735 x 11 + 544

Step 2: Since the reminder 735 ≠ 0, we apply division lemma to 544 and 735, to get

735 = 544 x 1 + 191

Step 3: We consider the new divisor 544 and the new remainder 191, and apply the division lemma to get

544 = 191 x 2 + 162

We consider the new divisor 191 and the new remainder 162,and apply the division lemma to get

191 = 162 x 1 + 29

We consider the new divisor 162 and the new remainder 29,and apply the division lemma to get

162 = 29 x 5 + 17

We consider the new divisor 29 and the new remainder 17,and apply the division lemma to get

29 = 17 x 1 + 12

We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get

17 = 12 x 1 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 735 and 8629 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(29,17) = HCF(162,29) = HCF(191,162) = HCF(544,191) = HCF(735,544) = HCF(8629,735) .

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Frequently Asked Questions on HCF of 735, 8629 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 735, 8629?

Answer: HCF of 735, 8629 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 735, 8629 using Euclid's Algorithm?

Answer: For arbitrary numbers 735, 8629 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.