Highest Common Factor of 902, 396, 391 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 902, 396, 391 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 902, 396, 391 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 902, 396, 391 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 902, 396, 391 is 1.

HCF(902, 396, 391) = 1

HCF of 902, 396, 391 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 902, 396, 391 is 1.

Highest Common Factor of 902,396,391 using Euclid's algorithm

Highest Common Factor of 902,396,391 is 1

Step 1: Since 902 > 396, we apply the division lemma to 902 and 396, to get

902 = 396 x 2 + 110

Step 2: Since the reminder 396 ≠ 0, we apply division lemma to 110 and 396, to get

396 = 110 x 3 + 66

Step 3: We consider the new divisor 110 and the new remainder 66, and apply the division lemma to get

110 = 66 x 1 + 44

We consider the new divisor 66 and the new remainder 44,and apply the division lemma to get

66 = 44 x 1 + 22

We consider the new divisor 44 and the new remainder 22,and apply the division lemma to get

44 = 22 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 902 and 396 is 22

Notice that 22 = HCF(44,22) = HCF(66,44) = HCF(110,66) = HCF(396,110) = HCF(902,396) .

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

Step 1: Since 391 > 22, we apply the division lemma to 391 and 22, to get

391 = 22 x 17 + 17

Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 17 and 22, to get

22 = 17 x 1 + 5

Step 3: We consider the new divisor 17 and the new remainder 5, and apply the division lemma to get

17 = 5 x 3 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 22 and 391 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(391,22) .

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Frequently Asked Questions on HCF of 902, 396, 391 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 902, 396, 391?

Answer: HCF of 902, 396, 391 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 902, 396, 391 using Euclid's Algorithm?

Answer: For arbitrary numbers 902, 396, 391 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.