Highest Common Factor of 442, 713 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 442, 713 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 442, 713 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 442, 713 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 442, 713 is 1.

HCF(442, 713) = 1

HCF of 442, 713 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 442, 713 is 1.

Highest Common Factor of 442,713 using Euclid's algorithm

Highest Common Factor of 442,713 is 1

Step 1: Since 713 > 442, we apply the division lemma to 713 and 442, to get

713 = 442 x 1 + 271

Step 2: Since the reminder 442 ≠ 0, we apply division lemma to 271 and 442, to get

442 = 271 x 1 + 171

Step 3: We consider the new divisor 271 and the new remainder 171, and apply the division lemma to get

271 = 171 x 1 + 100

We consider the new divisor 171 and the new remainder 100,and apply the division lemma to get

171 = 100 x 1 + 71

We consider the new divisor 100 and the new remainder 71,and apply the division lemma to get

100 = 71 x 1 + 29

We consider the new divisor 71 and the new remainder 29,and apply the division lemma to get

71 = 29 x 2 + 13

We consider the new divisor 29 and the new remainder 13,and apply the division lemma to get

29 = 13 x 2 + 3

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

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 442 and 713 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(29,13) = HCF(71,29) = HCF(100,71) = HCF(171,100) = HCF(271,171) = HCF(442,271) = HCF(713,442) .

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Frequently Asked Questions on HCF of 442, 713 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 442, 713?

Answer: HCF of 442, 713 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 442, 713 using Euclid's Algorithm?

Answer: For arbitrary numbers 442, 713 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.