Highest Common Factor of 8864, 7331, 31100 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 8864, 7331, 31100 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8864, 7331, 31100 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 8864, 7331, 31100 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 8864, 7331, 31100 is 1.

HCF(8864, 7331, 31100) = 1

HCF of 8864, 7331, 31100 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 8864, 7331, 31100 is 1.

Highest Common Factor of 8864,7331,31100 using Euclid's algorithm

Highest Common Factor of 8864,7331,31100 is 1

Step 1: Since 8864 > 7331, we apply the division lemma to 8864 and 7331, to get

8864 = 7331 x 1 + 1533

Step 2: Since the reminder 7331 ≠ 0, we apply division lemma to 1533 and 7331, to get

7331 = 1533 x 4 + 1199

Step 3: We consider the new divisor 1533 and the new remainder 1199, and apply the division lemma to get

1533 = 1199 x 1 + 334

We consider the new divisor 1199 and the new remainder 334,and apply the division lemma to get

1199 = 334 x 3 + 197

We consider the new divisor 334 and the new remainder 197,and apply the division lemma to get

334 = 197 x 1 + 137

We consider the new divisor 197 and the new remainder 137,and apply the division lemma to get

197 = 137 x 1 + 60

We consider the new divisor 137 and the new remainder 60,and apply the division lemma to get

137 = 60 x 2 + 17

We consider the new divisor 60 and the new remainder 17,and apply the division lemma to get

60 = 17 x 3 + 9

We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get

17 = 9 x 1 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8864 and 7331 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(60,17) = HCF(137,60) = HCF(197,137) = HCF(334,197) = HCF(1199,334) = HCF(1533,1199) = HCF(7331,1533) = HCF(8864,7331) .

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

Step 1: Since 31100 > 1, we apply the division lemma to 31100 and 1, to get

31100 = 1 x 31100 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31100 is 1

Notice that 1 = HCF(31100,1) .

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Frequently Asked Questions on HCF of 8864, 7331, 31100 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 8864, 7331, 31100?

Answer: HCF of 8864, 7331, 31100 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8864, 7331, 31100 using Euclid's Algorithm?

Answer: For arbitrary numbers 8864, 7331, 31100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.