Highest Common Factor of 172, 265, 671 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 172, 265, 671 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 172, 265, 671 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 172, 265, 671 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 172, 265, 671 is 1.

HCF(172, 265, 671) = 1

HCF of 172, 265, 671 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 172, 265, 671 is 1.

Highest Common Factor of 172,265,671 using Euclid's algorithm

Highest Common Factor of 172,265,671 is 1

Step 1: Since 265 > 172, we apply the division lemma to 265 and 172, to get

265 = 172 x 1 + 93

Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 93 and 172, to get

172 = 93 x 1 + 79

Step 3: We consider the new divisor 93 and the new remainder 79, and apply the division lemma to get

93 = 79 x 1 + 14

We consider the new divisor 79 and the new remainder 14,and apply the division lemma to get

79 = 14 x 5 + 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 172 and 265 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(79,14) = HCF(93,79) = HCF(172,93) = HCF(265,172) .

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

Step 1: Since 671 > 1, we apply the division lemma to 671 and 1, to get

671 = 1 x 671 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 671 is 1

Notice that 1 = HCF(671,1) .

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Frequently Asked Questions on HCF of 172, 265, 671 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 172, 265, 671?

Answer: HCF of 172, 265, 671 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 172, 265, 671 using Euclid's Algorithm?

Answer: For arbitrary numbers 172, 265, 671 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.