Highest Common Factor of 457, 749, 549 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 457, 749, 549 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 457, 749, 549 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 457, 749, 549 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 457, 749, 549 is 1.

HCF(457, 749, 549) = 1

HCF of 457, 749, 549 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 457, 749, 549 is 1.

Highest Common Factor of 457,749,549 using Euclid's algorithm

Highest Common Factor of 457,749,549 is 1

Step 1: Since 749 > 457, we apply the division lemma to 749 and 457, to get

749 = 457 x 1 + 292

Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 292 and 457, to get

457 = 292 x 1 + 165

Step 3: We consider the new divisor 292 and the new remainder 165, and apply the division lemma to get

292 = 165 x 1 + 127

We consider the new divisor 165 and the new remainder 127,and apply the division lemma to get

165 = 127 x 1 + 38

We consider the new divisor 127 and the new remainder 38,and apply the division lemma to get

127 = 38 x 3 + 13

We consider the new divisor 38 and the new remainder 13,and apply the division lemma to get

38 = 13 x 2 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 457 and 749 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(38,13) = HCF(127,38) = HCF(165,127) = HCF(292,165) = HCF(457,292) = HCF(749,457) .

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

Step 1: Since 549 > 1, we apply the division lemma to 549 and 1, to get

549 = 1 x 549 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 549 is 1

Notice that 1 = HCF(549,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 457, 749, 549 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 457, 749, 549?

Answer: HCF of 457, 749, 549 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 457, 749, 549 using Euclid's Algorithm?

Answer: For arbitrary numbers 457, 749, 549 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.