Highest Common Factor of 177, 688, 722 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, 688, 722 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 177, 688, 722 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, 688, 722 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, 688, 722 is 1.

HCF(177, 688, 722) = 1

HCF of 177, 688, 722 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, 688, 722 is 1.

Highest Common Factor of 177,688,722 using Euclid's algorithm

Highest Common Factor of 177,688,722 is 1

Step 1: Since 688 > 177, we apply the division lemma to 688 and 177, to get

688 = 177 x 3 + 157

Step 2: Since the reminder 177 ≠ 0, we apply division lemma to 157 and 177, to get

177 = 157 x 1 + 20

Step 3: We consider the new divisor 157 and the new remainder 20, and apply the division lemma to get

157 = 20 x 7 + 17

We consider the new divisor 20 and the new remainder 17,and apply the division lemma to get

20 = 17 x 1 + 3

We consider the new divisor 17 and the new remainder 3,and apply the division lemma to get

17 = 3 x 5 + 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 688 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(20,17) = HCF(157,20) = HCF(177,157) = HCF(688,177) .

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

Step 1: Since 722 > 1, we apply the division lemma to 722 and 1, to get

722 = 1 x 722 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 722 is 1

Notice that 1 = HCF(722,1) .

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Frequently Asked Questions on HCF of 177, 688, 722 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, 688, 722?

Answer: HCF of 177, 688, 722 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 177, 688, 722 using Euclid's Algorithm?

Answer: For arbitrary numbers 177, 688, 722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.