Highest Common Factor of 3116, 8175, 51122 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 3116, 8175, 51122 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3116, 8175, 51122 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 3116, 8175, 51122 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 3116, 8175, 51122 is 1.

HCF(3116, 8175, 51122) = 1

HCF of 3116, 8175, 51122 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 3116, 8175, 51122 is 1.

Highest Common Factor of 3116,8175,51122 using Euclid's algorithm

Highest Common Factor of 3116,8175,51122 is 1

Step 1: Since 8175 > 3116, we apply the division lemma to 8175 and 3116, to get

8175 = 3116 x 2 + 1943

Step 2: Since the reminder 3116 ≠ 0, we apply division lemma to 1943 and 3116, to get

3116 = 1943 x 1 + 1173

Step 3: We consider the new divisor 1943 and the new remainder 1173, and apply the division lemma to get

1943 = 1173 x 1 + 770

We consider the new divisor 1173 and the new remainder 770,and apply the division lemma to get

1173 = 770 x 1 + 403

We consider the new divisor 770 and the new remainder 403,and apply the division lemma to get

770 = 403 x 1 + 367

We consider the new divisor 403 and the new remainder 367,and apply the division lemma to get

403 = 367 x 1 + 36

We consider the new divisor 367 and the new remainder 36,and apply the division lemma to get

367 = 36 x 10 + 7

We consider the new divisor 36 and the new remainder 7,and apply the division lemma to get

36 = 7 x 5 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3116 and 8175 is 1

Notice that 1 = HCF(7,1) = HCF(36,7) = HCF(367,36) = HCF(403,367) = HCF(770,403) = HCF(1173,770) = HCF(1943,1173) = HCF(3116,1943) = HCF(8175,3116) .

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

Step 1: Since 51122 > 1, we apply the division lemma to 51122 and 1, to get

51122 = 1 x 51122 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51122 is 1

Notice that 1 = HCF(51122,1) .

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Frequently Asked Questions on HCF of 3116, 8175, 51122 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 3116, 8175, 51122?

Answer: HCF of 3116, 8175, 51122 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3116, 8175, 51122 using Euclid's Algorithm?

Answer: For arbitrary numbers 3116, 8175, 51122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.