Highest Common Factor of 657, 420, 964, 12 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, 420, 964, 12 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 657, 420, 964, 12 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, 420, 964, 12 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, 420, 964, 12 is 1.

HCF(657, 420, 964, 12) = 1

HCF of 657, 420, 964, 12 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, 420, 964, 12 is 1.

Highest Common Factor of 657,420,964,12 using Euclid's algorithm

Highest Common Factor of 657,420,964,12 is 1

Step 1: Since 657 > 420, we apply the division lemma to 657 and 420, to get

657 = 420 x 1 + 237

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 237 and 420, to get

420 = 237 x 1 + 183

Step 3: We consider the new divisor 237 and the new remainder 183, and apply the division lemma to get

237 = 183 x 1 + 54

We consider the new divisor 183 and the new remainder 54,and apply the division lemma to get

183 = 54 x 3 + 21

We consider the new divisor 54 and the new remainder 21,and apply the division lemma to get

54 = 21 x 2 + 12

We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get

21 = 12 x 1 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 657 and 420 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(54,21) = HCF(183,54) = HCF(237,183) = HCF(420,237) = HCF(657,420) .

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

Step 1: Since 964 > 3, we apply the division lemma to 964 and 3, to get

964 = 3 x 321 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 964 is 1

Notice that 1 = HCF(3,1) = HCF(964,3) .

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

Step 1: Since 12 > 1, we apply the division lemma to 12 and 1, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12 is 1

Notice that 1 = HCF(12,1) .

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Frequently Asked Questions on HCF of 657, 420, 964, 12 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, 420, 964, 12?

Answer: HCF of 657, 420, 964, 12 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 657, 420, 964, 12 using Euclid's Algorithm?

Answer: For arbitrary numbers 657, 420, 964, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.