Highest Common Factor of 596, 977, 177 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 596, 977, 177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 596, 977, 177 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 596, 977, 177 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 596, 977, 177 is 1.

HCF(596, 977, 177) = 1

HCF of 596, 977, 177 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 596, 977, 177 is 1.

Highest Common Factor of 596,977,177 using Euclid's algorithm

Highest Common Factor of 596,977,177 is 1

Step 1: Since 977 > 596, we apply the division lemma to 977 and 596, to get

977 = 596 x 1 + 381

Step 2: Since the reminder 596 ≠ 0, we apply division lemma to 381 and 596, to get

596 = 381 x 1 + 215

Step 3: We consider the new divisor 381 and the new remainder 215, and apply the division lemma to get

381 = 215 x 1 + 166

We consider the new divisor 215 and the new remainder 166,and apply the division lemma to get

215 = 166 x 1 + 49

We consider the new divisor 166 and the new remainder 49,and apply the division lemma to get

166 = 49 x 3 + 19

We consider the new divisor 49 and the new remainder 19,and apply the division lemma to get

49 = 19 x 2 + 11

We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 596 and 977 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(49,19) = HCF(166,49) = HCF(215,166) = HCF(381,215) = HCF(596,381) = HCF(977,596) .

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

Step 1: Since 177 > 1, we apply the division lemma to 177 and 1, to get

177 = 1 x 177 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 177 is 1

Notice that 1 = HCF(177,1) .

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Frequently Asked Questions on HCF of 596, 977, 177 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 596, 977, 177?

Answer: HCF of 596, 977, 177 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 596, 977, 177 using Euclid's Algorithm?

Answer: For arbitrary numbers 596, 977, 177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.