Highest Common Factor of 177, 659, 724 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, 659, 724 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 177, 659, 724 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, 659, 724 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, 659, 724 is 1.

HCF(177, 659, 724) = 1

HCF of 177, 659, 724 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, 659, 724 is 1.

Highest Common Factor of 177,659,724 using Euclid's algorithm

Highest Common Factor of 177,659,724 is 1

Step 1: Since 659 > 177, we apply the division lemma to 659 and 177, to get

659 = 177 x 3 + 128

Step 2: Since the reminder 177 ≠ 0, we apply division lemma to 128 and 177, to get

177 = 128 x 1 + 49

Step 3: We consider the new divisor 128 and the new remainder 49, and apply the division lemma to get

128 = 49 x 2 + 30

We consider the new divisor 49 and the new remainder 30,and apply the division lemma to get

49 = 30 x 1 + 19

We consider the new divisor 30 and the new remainder 19,and apply the division lemma to get

30 = 19 x 1 + 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 177 and 659 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(30,19) = HCF(49,30) = HCF(128,49) = HCF(177,128) = HCF(659,177) .

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

Step 1: Since 724 > 1, we apply the division lemma to 724 and 1, to get

724 = 1 x 724 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 724 is 1

Notice that 1 = HCF(724,1) .

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Frequently Asked Questions on HCF of 177, 659, 724 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, 659, 724?

Answer: HCF of 177, 659, 724 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 177, 659, 724 using Euclid's Algorithm?

Answer: For arbitrary numbers 177, 659, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.