Highest Common Factor of 76, 173, 662 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 76, 173, 662 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 76, 173, 662 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 76, 173, 662 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 76, 173, 662 is 1.

HCF(76, 173, 662) = 1

HCF of 76, 173, 662 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 76, 173, 662 is 1.

Highest Common Factor of 76,173,662 using Euclid's algorithm

Highest Common Factor of 76,173,662 is 1

Step 1: Since 173 > 76, we apply the division lemma to 173 and 76, to get

173 = 76 x 2 + 21

Step 2: Since the reminder 76 ≠ 0, we apply division lemma to 21 and 76, to get

76 = 21 x 3 + 13

Step 3: We consider the new divisor 21 and the new remainder 13, and apply the division lemma to get

21 = 13 x 1 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 76 and 173 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(76,21) = HCF(173,76) .

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

Step 1: Since 662 > 1, we apply the division lemma to 662 and 1, to get

662 = 1 x 662 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 662 is 1

Notice that 1 = HCF(662,1) .

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Frequently Asked Questions on HCF of 76, 173, 662 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 76, 173, 662?

Answer: HCF of 76, 173, 662 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 76, 173, 662 using Euclid's Algorithm?

Answer: For arbitrary numbers 76, 173, 662 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.