Highest Common Factor of 177, 517, 732 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 177, 517, 732 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 177, 517, 732 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 177, 517, 732 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 177, 517, 732 is 1.

HCF(177, 517, 732) = 1

HCF of 177, 517, 732 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 177, 517, 732 is 1.

Highest Common Factor of 177,517,732 using Euclid's algorithm

Highest Common Factor of 177,517,732 is 1

Step 1: Since 517 > 177, we apply the division lemma to 517 and 177, to get

517 = 177 x 2 + 163

Step 2: Since the reminder 177 ≠ 0, we apply division lemma to 163 and 177, to get

177 = 163 x 1 + 14

Step 3: We consider the new divisor 163 and the new remainder 14, and apply the division lemma to get

163 = 14 x 11 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 177 and 517 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(163,14) = HCF(177,163) = HCF(517,177) .

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

Step 1: Since 732 > 1, we apply the division lemma to 732 and 1, to get

732 = 1 x 732 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 732 is 1

Notice that 1 = HCF(732,1) .

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Frequently Asked Questions on HCF of 177, 517, 732 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 177, 517, 732?

Answer: HCF of 177, 517, 732 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 177, 517, 732 using Euclid's Algorithm?

Answer: For arbitrary numbers 177, 517, 732 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.