Highest Common Factor of 910, 1658 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 910, 1658 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 910, 1658 is 2 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 910, 1658 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 910, 1658 is 2.

HCF(910, 1658) = 2

HCF of 910, 1658 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 910, 1658 is 2.

Highest Common Factor of 910,1658 using Euclid's algorithm

Highest Common Factor of 910,1658 is 2

Step 1: Since 1658 > 910, we apply the division lemma to 1658 and 910, to get

1658 = 910 x 1 + 748

Step 2: Since the reminder 910 ≠ 0, we apply division lemma to 748 and 910, to get

910 = 748 x 1 + 162

Step 3: We consider the new divisor 748 and the new remainder 162, and apply the division lemma to get

748 = 162 x 4 + 100

We consider the new divisor 162 and the new remainder 100,and apply the division lemma to get

162 = 100 x 1 + 62

We consider the new divisor 100 and the new remainder 62,and apply the division lemma to get

100 = 62 x 1 + 38

We consider the new divisor 62 and the new remainder 38,and apply the division lemma to get

62 = 38 x 1 + 24

We consider the new divisor 38 and the new remainder 24,and apply the division lemma to get

38 = 24 x 1 + 14

We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get

24 = 14 x 1 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 910 and 1658 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(38,24) = HCF(62,38) = HCF(100,62) = HCF(162,100) = HCF(748,162) = HCF(910,748) = HCF(1658,910) .

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Frequently Asked Questions on HCF of 910, 1658 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 910, 1658?

Answer: HCF of 910, 1658 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 910, 1658 using Euclid's Algorithm?

Answer: For arbitrary numbers 910, 1658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.