Highest Common Factor of 657, 612, 490 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 657, 612, 490 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 657, 612, 490 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 657, 612, 490 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 657, 612, 490 is 1.

HCF(657, 612, 490) = 1

HCF of 657, 612, 490 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 657, 612, 490 is 1.

Highest Common Factor of 657,612,490 using Euclid's algorithm

Highest Common Factor of 657,612,490 is 1

Step 1: Since 657 > 612, we apply the division lemma to 657 and 612, to get

657 = 612 x 1 + 45

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 45 and 612, to get

612 = 45 x 13 + 27

Step 3: We consider the new divisor 45 and the new remainder 27, and apply the division lemma to get

45 = 27 x 1 + 18

We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get

27 = 18 x 1 + 9

We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get

18 = 9 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 657 and 612 is 9

Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(45,27) = HCF(612,45) = HCF(657,612) .

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

Step 1: Since 490 > 9, we apply the division lemma to 490 and 9, to get

490 = 9 x 54 + 4

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 4 and 9, to get

9 = 4 x 2 + 1

Step 3: 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 9 and 490 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(490,9) .

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Frequently Asked Questions on HCF of 657, 612, 490 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 657, 612, 490?

Answer: HCF of 657, 612, 490 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 657, 612, 490 using Euclid's Algorithm?

Answer: For arbitrary numbers 657, 612, 490 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.