Highest Common Factor of 386, 972, 769 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 386, 972, 769 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 386, 972, 769 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 386, 972, 769 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 386, 972, 769 is 1.

HCF(386, 972, 769) = 1

HCF of 386, 972, 769 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 386, 972, 769 is 1.

Highest Common Factor of 386,972,769 using Euclid's algorithm

Highest Common Factor of 386,972,769 is 1

Step 1: Since 972 > 386, we apply the division lemma to 972 and 386, to get

972 = 386 x 2 + 200

Step 2: Since the reminder 386 ≠ 0, we apply division lemma to 200 and 386, to get

386 = 200 x 1 + 186

Step 3: We consider the new divisor 200 and the new remainder 186, and apply the division lemma to get

200 = 186 x 1 + 14

We consider the new divisor 186 and the new remainder 14,and apply the division lemma to get

186 = 14 x 13 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 386 and 972 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(186,14) = HCF(200,186) = HCF(386,200) = HCF(972,386) .

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

Step 1: Since 769 > 2, we apply the division lemma to 769 and 2, to get

769 = 2 x 384 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 769 is 1

Notice that 1 = HCF(2,1) = HCF(769,2) .

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Frequently Asked Questions on HCF of 386, 972, 769 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 386, 972, 769?

Answer: HCF of 386, 972, 769 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 386, 972, 769 using Euclid's Algorithm?

Answer: For arbitrary numbers 386, 972, 769 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.