Highest Common Factor of 548, 649 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 548, 649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 548, 649 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 548, 649 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 548, 649 is 1.

HCF(548, 649) = 1

HCF of 548, 649 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 548, 649 is 1.

Highest Common Factor of 548,649 using Euclid's algorithm

Highest Common Factor of 548,649 is 1

Step 1: Since 649 > 548, we apply the division lemma to 649 and 548, to get

649 = 548 x 1 + 101

Step 2: Since the reminder 548 ≠ 0, we apply division lemma to 101 and 548, to get

548 = 101 x 5 + 43

Step 3: We consider the new divisor 101 and the new remainder 43, and apply the division lemma to get

101 = 43 x 2 + 15

We consider the new divisor 43 and the new remainder 15,and apply the division lemma to get

43 = 15 x 2 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 548 and 649 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(43,15) = HCF(101,43) = HCF(548,101) = HCF(649,548) .

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Frequently Asked Questions on HCF of 548, 649 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 548, 649?

Answer: HCF of 548, 649 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 548, 649 using Euclid's Algorithm?

Answer: For arbitrary numbers 548, 649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.