Highest Common Factor of 713, 370 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 713, 370 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 713, 370 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 713, 370 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 713, 370 is 1.

HCF(713, 370) = 1

HCF of 713, 370 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 713, 370 is 1.

Highest Common Factor of 713,370 using Euclid's algorithm

Highest Common Factor of 713,370 is 1

Step 1: Since 713 > 370, we apply the division lemma to 713 and 370, to get

713 = 370 x 1 + 343

Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 343 and 370, to get

370 = 343 x 1 + 27

Step 3: We consider the new divisor 343 and the new remainder 27, and apply the division lemma to get

343 = 27 x 12 + 19

We consider the new divisor 27 and the new remainder 19,and apply the division lemma to get

27 = 19 x 1 + 8

We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get

19 = 8 x 2 + 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 713 and 370 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(343,27) = HCF(370,343) = HCF(713,370) .

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Frequently Asked Questions on HCF of 713, 370 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 713, 370?

Answer: HCF of 713, 370 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 713, 370 using Euclid's Algorithm?

Answer: For arbitrary numbers 713, 370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.