Highest Common Factor of 9952, 3708, 56765 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 9952, 3708, 56765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9952, 3708, 56765 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 9952, 3708, 56765 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 9952, 3708, 56765 is 1.

HCF(9952, 3708, 56765) = 1

HCF of 9952, 3708, 56765 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 9952, 3708, 56765 is 1.

Highest Common Factor of 9952,3708,56765 using Euclid's algorithm

Highest Common Factor of 9952,3708,56765 is 1

Step 1: Since 9952 > 3708, we apply the division lemma to 9952 and 3708, to get

9952 = 3708 x 2 + 2536

Step 2: Since the reminder 3708 ≠ 0, we apply division lemma to 2536 and 3708, to get

3708 = 2536 x 1 + 1172

Step 3: We consider the new divisor 2536 and the new remainder 1172, and apply the division lemma to get

2536 = 1172 x 2 + 192

We consider the new divisor 1172 and the new remainder 192,and apply the division lemma to get

1172 = 192 x 6 + 20

We consider the new divisor 192 and the new remainder 20,and apply the division lemma to get

192 = 20 x 9 + 12

We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get

20 = 12 x 1 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 9952 and 3708 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(192,20) = HCF(1172,192) = HCF(2536,1172) = HCF(3708,2536) = HCF(9952,3708) .

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

Step 1: Since 56765 > 4, we apply the division lemma to 56765 and 4, to get

56765 = 4 x 14191 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 56765 is 1

Notice that 1 = HCF(4,1) = HCF(56765,4) .

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Frequently Asked Questions on HCF of 9952, 3708, 56765 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 9952, 3708, 56765?

Answer: HCF of 9952, 3708, 56765 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9952, 3708, 56765 using Euclid's Algorithm?

Answer: For arbitrary numbers 9952, 3708, 56765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.