Highest Common Factor of 460, 749, 462 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 460, 749, 462 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 460, 749, 462 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 460, 749, 462 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 460, 749, 462 is 1.

HCF(460, 749, 462) = 1

HCF of 460, 749, 462 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 460, 749, 462 is 1.

Highest Common Factor of 460,749,462 using Euclid's algorithm

Highest Common Factor of 460,749,462 is 1

Step 1: Since 749 > 460, we apply the division lemma to 749 and 460, to get

749 = 460 x 1 + 289

Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 289 and 460, to get

460 = 289 x 1 + 171

Step 3: We consider the new divisor 289 and the new remainder 171, and apply the division lemma to get

289 = 171 x 1 + 118

We consider the new divisor 171 and the new remainder 118,and apply the division lemma to get

171 = 118 x 1 + 53

We consider the new divisor 118 and the new remainder 53,and apply the division lemma to get

118 = 53 x 2 + 12

We consider the new divisor 53 and the new remainder 12,and apply the division lemma to get

53 = 12 x 4 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 460 and 749 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(53,12) = HCF(118,53) = HCF(171,118) = HCF(289,171) = HCF(460,289) = HCF(749,460) .

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

Step 1: Since 462 > 1, we apply the division lemma to 462 and 1, to get

462 = 1 x 462 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 462 is 1

Notice that 1 = HCF(462,1) .

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Frequently Asked Questions on HCF of 460, 749, 462 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 460, 749, 462?

Answer: HCF of 460, 749, 462 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 460, 749, 462 using Euclid's Algorithm?

Answer: For arbitrary numbers 460, 749, 462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.