Highest Common Factor of 6957, 6144, 61249 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 6957, 6144, 61249 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6957, 6144, 61249 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 6957, 6144, 61249 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 6957, 6144, 61249 is 1.

HCF(6957, 6144, 61249) = 1

HCF of 6957, 6144, 61249 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 6957, 6144, 61249 is 1.

Highest Common Factor of 6957,6144,61249 using Euclid's algorithm

Highest Common Factor of 6957,6144,61249 is 1

Step 1: Since 6957 > 6144, we apply the division lemma to 6957 and 6144, to get

6957 = 6144 x 1 + 813

Step 2: Since the reminder 6144 ≠ 0, we apply division lemma to 813 and 6144, to get

6144 = 813 x 7 + 453

Step 3: We consider the new divisor 813 and the new remainder 453, and apply the division lemma to get

813 = 453 x 1 + 360

We consider the new divisor 453 and the new remainder 360,and apply the division lemma to get

453 = 360 x 1 + 93

We consider the new divisor 360 and the new remainder 93,and apply the division lemma to get

360 = 93 x 3 + 81

We consider the new divisor 93 and the new remainder 81,and apply the division lemma to get

93 = 81 x 1 + 12

We consider the new divisor 81 and the new remainder 12,and apply the division lemma to get

81 = 12 x 6 + 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 6957 and 6144 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(81,12) = HCF(93,81) = HCF(360,93) = HCF(453,360) = HCF(813,453) = HCF(6144,813) = HCF(6957,6144) .

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

Step 1: Since 61249 > 3, we apply the division lemma to 61249 and 3, to get

61249 = 3 x 20416 + 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 61249 is 1

Notice that 1 = HCF(3,1) = HCF(61249,3) .

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Frequently Asked Questions on HCF of 6957, 6144, 61249 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 6957, 6144, 61249?

Answer: HCF of 6957, 6144, 61249 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6957, 6144, 61249 using Euclid's Algorithm?

Answer: For arbitrary numbers 6957, 6144, 61249 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.