Highest Common Factor of 1057, 7696, 46416 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 1057, 7696, 46416 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1057, 7696, 46416 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 1057, 7696, 46416 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 1057, 7696, 46416 is 1.

HCF(1057, 7696, 46416) = 1

HCF of 1057, 7696, 46416 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 1057, 7696, 46416 is 1.

Highest Common Factor of 1057,7696,46416 using Euclid's algorithm

Highest Common Factor of 1057,7696,46416 is 1

Step 1: Since 7696 > 1057, we apply the division lemma to 7696 and 1057, to get

7696 = 1057 x 7 + 297

Step 2: Since the reminder 1057 ≠ 0, we apply division lemma to 297 and 1057, to get

1057 = 297 x 3 + 166

Step 3: We consider the new divisor 297 and the new remainder 166, and apply the division lemma to get

297 = 166 x 1 + 131

We consider the new divisor 166 and the new remainder 131,and apply the division lemma to get

166 = 131 x 1 + 35

We consider the new divisor 131 and the new remainder 35,and apply the division lemma to get

131 = 35 x 3 + 26

We consider the new divisor 35 and the new remainder 26,and apply the division lemma to get

35 = 26 x 1 + 9

We consider the new divisor 26 and the new remainder 9,and apply the division lemma to get

26 = 9 x 2 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1057 and 7696 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(26,9) = HCF(35,26) = HCF(131,35) = HCF(166,131) = HCF(297,166) = HCF(1057,297) = HCF(7696,1057) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 46416 > 1, we apply the division lemma to 46416 and 1, to get

46416 = 1 x 46416 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 46416 is 1

Notice that 1 = HCF(46416,1) .

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Frequently Asked Questions on HCF of 1057, 7696, 46416 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 1057, 7696, 46416?

Answer: HCF of 1057, 7696, 46416 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1057, 7696, 46416 using Euclid's Algorithm?

Answer: For arbitrary numbers 1057, 7696, 46416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.