Highest Common Factor of 930, 682, 765 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 930, 682, 765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 930, 682, 765 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 930, 682, 765 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 930, 682, 765 is 1.

HCF(930, 682, 765) = 1

HCF of 930, 682, 765 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 930, 682, 765 is 1.

Highest Common Factor of 930,682,765 using Euclid's algorithm

Highest Common Factor of 930,682,765 is 1

Step 1: Since 930 > 682, we apply the division lemma to 930 and 682, to get

930 = 682 x 1 + 248

Step 2: Since the reminder 682 ≠ 0, we apply division lemma to 248 and 682, to get

682 = 248 x 2 + 186

Step 3: We consider the new divisor 248 and the new remainder 186, and apply the division lemma to get

248 = 186 x 1 + 62

We consider the new divisor 186 and the new remainder 62, and apply the division lemma to get

186 = 62 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 62, the HCF of 930 and 682 is 62

Notice that 62 = HCF(186,62) = HCF(248,186) = HCF(682,248) = HCF(930,682) .

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

Step 1: Since 765 > 62, we apply the division lemma to 765 and 62, to get

765 = 62 x 12 + 21

Step 2: Since the reminder 62 ≠ 0, we apply division lemma to 21 and 62, to get

62 = 21 x 2 + 20

Step 3: We consider the new divisor 21 and the new remainder 20, and apply the division lemma to get

21 = 20 x 1 + 1

We consider the new divisor 20 and the new remainder 1, and apply the division lemma to get

20 = 1 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 62 and 765 is 1

Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(62,21) = HCF(765,62) .

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Frequently Asked Questions on HCF of 930, 682, 765 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 930, 682, 765?

Answer: HCF of 930, 682, 765 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 930, 682, 765 using Euclid's Algorithm?

Answer: For arbitrary numbers 930, 682, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.