Highest Common Factor of 988, 302, 665 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 988, 302, 665 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 988, 302, 665 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 988, 302, 665 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 988, 302, 665 is 1.

HCF(988, 302, 665) = 1

HCF of 988, 302, 665 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 988, 302, 665 is 1.

Highest Common Factor of 988,302,665 using Euclid's algorithm

Highest Common Factor of 988,302,665 is 1

Step 1: Since 988 > 302, we apply the division lemma to 988 and 302, to get

988 = 302 x 3 + 82

Step 2: Since the reminder 302 ≠ 0, we apply division lemma to 82 and 302, to get

302 = 82 x 3 + 56

Step 3: We consider the new divisor 82 and the new remainder 56, and apply the division lemma to get

82 = 56 x 1 + 26

We consider the new divisor 56 and the new remainder 26,and apply the division lemma to get

56 = 26 x 2 + 4

We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get

26 = 4 x 6 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 988 and 302 is 2

Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(56,26) = HCF(82,56) = HCF(302,82) = HCF(988,302) .

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

Step 1: Since 665 > 2, we apply the division lemma to 665 and 2, to get

665 = 2 x 332 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 665 is 1

Notice that 1 = HCF(2,1) = HCF(665,2) .

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Frequently Asked Questions on HCF of 988, 302, 665 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 988, 302, 665?

Answer: HCF of 988, 302, 665 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 988, 302, 665 using Euclid's Algorithm?

Answer: For arbitrary numbers 988, 302, 665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.