Highest Common Factor of 656, 473, 388 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, 473, 388 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 656, 473, 388 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, 473, 388 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, 473, 388 is 1.

HCF(656, 473, 388) = 1

HCF of 656, 473, 388 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, 473, 388 is 1.

Highest Common Factor of 656,473,388 using Euclid's algorithm

Highest Common Factor of 656,473,388 is 1

Step 1: Since 656 > 473, we apply the division lemma to 656 and 473, to get

656 = 473 x 1 + 183

Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 183 and 473, to get

473 = 183 x 2 + 107

Step 3: We consider the new divisor 183 and the new remainder 107, and apply the division lemma to get

183 = 107 x 1 + 76

We consider the new divisor 107 and the new remainder 76,and apply the division lemma to get

107 = 76 x 1 + 31

We consider the new divisor 76 and the new remainder 31,and apply the division lemma to get

76 = 31 x 2 + 14

We consider the new divisor 31 and the new remainder 14,and apply the division lemma to get

31 = 14 x 2 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 656 and 473 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(76,31) = HCF(107,76) = HCF(183,107) = HCF(473,183) = HCF(656,473) .

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

Step 1: Since 388 > 1, we apply the division lemma to 388 and 1, to get

388 = 1 x 388 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 388 is 1

Notice that 1 = HCF(388,1) .

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Frequently Asked Questions on HCF of 656, 473, 388 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, 473, 388?

Answer: HCF of 656, 473, 388 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 656, 473, 388 using Euclid's Algorithm?

Answer: For arbitrary numbers 656, 473, 388 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.