Highest Common Factor of 616, 961, 138 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 616, 961, 138 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 616, 961, 138 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 616, 961, 138 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 616, 961, 138 is 1.

HCF(616, 961, 138) = 1

HCF of 616, 961, 138 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 616, 961, 138 is 1.

Highest Common Factor of 616,961,138 using Euclid's algorithm

Highest Common Factor of 616,961,138 is 1

Step 1: Since 961 > 616, we apply the division lemma to 961 and 616, to get

961 = 616 x 1 + 345

Step 2: Since the reminder 616 ≠ 0, we apply division lemma to 345 and 616, to get

616 = 345 x 1 + 271

Step 3: We consider the new divisor 345 and the new remainder 271, and apply the division lemma to get

345 = 271 x 1 + 74

We consider the new divisor 271 and the new remainder 74,and apply the division lemma to get

271 = 74 x 3 + 49

We consider the new divisor 74 and the new remainder 49,and apply the division lemma to get

74 = 49 x 1 + 25

We consider the new divisor 49 and the new remainder 25,and apply the division lemma to get

49 = 25 x 1 + 24

We consider the new divisor 25 and the new remainder 24,and apply the division lemma to get

25 = 24 x 1 + 1

We consider the new divisor 24 and the new remainder 1,and apply the division lemma to get

24 = 1 x 24 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 616 and 961 is 1

Notice that 1 = HCF(24,1) = HCF(25,24) = HCF(49,25) = HCF(74,49) = HCF(271,74) = HCF(345,271) = HCF(616,345) = HCF(961,616) .

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

Step 1: Since 138 > 1, we apply the division lemma to 138 and 1, to get

138 = 1 x 138 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 138 is 1

Notice that 1 = HCF(138,1) .

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Frequently Asked Questions on HCF of 616, 961, 138 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 616, 961, 138?

Answer: HCF of 616, 961, 138 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 616, 961, 138 using Euclid's Algorithm?

Answer: For arbitrary numbers 616, 961, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.