Highest Common Factor of 692, 31035 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 692, 31035 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 692, 31035 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 692, 31035 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 692, 31035 is 1.

HCF(692, 31035) = 1

HCF of 692, 31035 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 692, 31035 is 1.

Highest Common Factor of 692,31035 using Euclid's algorithm

Highest Common Factor of 692,31035 is 1

Step 1: Since 31035 > 692, we apply the division lemma to 31035 and 692, to get

31035 = 692 x 44 + 587

Step 2: Since the reminder 692 ≠ 0, we apply division lemma to 587 and 692, to get

692 = 587 x 1 + 105

Step 3: We consider the new divisor 587 and the new remainder 105, and apply the division lemma to get

587 = 105 x 5 + 62

We consider the new divisor 105 and the new remainder 62,and apply the division lemma to get

105 = 62 x 1 + 43

We consider the new divisor 62 and the new remainder 43,and apply the division lemma to get

62 = 43 x 1 + 19

We consider the new divisor 43 and the new remainder 19,and apply the division lemma to get

43 = 19 x 2 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 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 692 and 31035 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(43,19) = HCF(62,43) = HCF(105,62) = HCF(587,105) = HCF(692,587) = HCF(31035,692) .

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Frequently Asked Questions on HCF of 692, 31035 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 692, 31035?

Answer: HCF of 692, 31035 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 692, 31035 using Euclid's Algorithm?

Answer: For arbitrary numbers 692, 31035 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.