Highest Common Factor of 462, 658, 657 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 462, 658, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 462, 658, 657 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 462, 658, 657 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 462, 658, 657 is 1.

HCF(462, 658, 657) = 1

HCF of 462, 658, 657 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 462, 658, 657 is 1.

Highest Common Factor of 462,658,657 using Euclid's algorithm

Highest Common Factor of 462,658,657 is 1

Step 1: Since 658 > 462, we apply the division lemma to 658 and 462, to get

658 = 462 x 1 + 196

Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 196 and 462, to get

462 = 196 x 2 + 70

Step 3: We consider the new divisor 196 and the new remainder 70, and apply the division lemma to get

196 = 70 x 2 + 56

We consider the new divisor 70 and the new remainder 56,and apply the division lemma to get

70 = 56 x 1 + 14

We consider the new divisor 56 and the new remainder 14,and apply the division lemma to get

56 = 14 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 462 and 658 is 14

Notice that 14 = HCF(56,14) = HCF(70,56) = HCF(196,70) = HCF(462,196) = HCF(658,462) .

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

Step 1: Since 657 > 14, we apply the division lemma to 657 and 14, to get

657 = 14 x 46 + 13

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 13 and 14, to get

14 = 13 x 1 + 1

Step 3: We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 657 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(657,14) .

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Frequently Asked Questions on HCF of 462, 658, 657 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 462, 658, 657?

Answer: HCF of 462, 658, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 462, 658, 657 using Euclid's Algorithm?

Answer: For arbitrary numbers 462, 658, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.