Highest Common Factor of 656, 277, 342 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 656, 277, 342 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 656, 277, 342 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 656, 277, 342 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 656, 277, 342 is 1.

HCF(656, 277, 342) = 1

HCF of 656, 277, 342 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 656, 277, 342 is 1.

Highest Common Factor of 656,277,342 using Euclid's algorithm

Highest Common Factor of 656,277,342 is 1

Step 1: Since 656 > 277, we apply the division lemma to 656 and 277, to get

656 = 277 x 2 + 102

Step 2: Since the reminder 277 ≠ 0, we apply division lemma to 102 and 277, to get

277 = 102 x 2 + 73

Step 3: We consider the new divisor 102 and the new remainder 73, and apply the division lemma to get

102 = 73 x 1 + 29

We consider the new divisor 73 and the new remainder 29,and apply the division lemma to get

73 = 29 x 2 + 15

We consider the new divisor 29 and the new remainder 15,and apply the division lemma to get

29 = 15 x 1 + 14

We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 656 and 277 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(29,15) = HCF(73,29) = HCF(102,73) = HCF(277,102) = HCF(656,277) .

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

Step 1: Since 342 > 1, we apply the division lemma to 342 and 1, to get

342 = 1 x 342 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 342 is 1

Notice that 1 = HCF(342,1) .

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Frequently Asked Questions on HCF of 656, 277, 342 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 656, 277, 342?

Answer: HCF of 656, 277, 342 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 656, 277, 342 using Euclid's Algorithm?

Answer: For arbitrary numbers 656, 277, 342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.