Highest Common Factor of 649, 392 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 649, 392 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 649, 392 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 649, 392 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 649, 392 is 1.

HCF(649, 392) = 1

HCF of 649, 392 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 649, 392 is 1.

Highest Common Factor of 649,392 using Euclid's algorithm

Highest Common Factor of 649,392 is 1

Step 1: Since 649 > 392, we apply the division lemma to 649 and 392, to get

649 = 392 x 1 + 257

Step 2: Since the reminder 392 ≠ 0, we apply division lemma to 257 and 392, to get

392 = 257 x 1 + 135

Step 3: We consider the new divisor 257 and the new remainder 135, and apply the division lemma to get

257 = 135 x 1 + 122

We consider the new divisor 135 and the new remainder 122,and apply the division lemma to get

135 = 122 x 1 + 13

We consider the new divisor 122 and the new remainder 13,and apply the division lemma to get

122 = 13 x 9 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 649 and 392 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(122,13) = HCF(135,122) = HCF(257,135) = HCF(392,257) = HCF(649,392) .

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Frequently Asked Questions on HCF of 649, 392 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 649, 392?

Answer: HCF of 649, 392 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 649, 392 using Euclid's Algorithm?

Answer: For arbitrary numbers 649, 392 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.