Highest Common Factor of 462, 752, 431 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 462, 752, 431 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 462, 752, 431 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 462, 752, 431 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 462, 752, 431 is 1.

HCF(462, 752, 431) = 1

HCF of 462, 752, 431 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 462, 752, 431 is 1.

Highest Common Factor of 462,752,431 using Euclid's algorithm

Highest Common Factor of 462,752,431 is 1

Step 1: Since 752 > 462, we apply the division lemma to 752 and 462, to get

752 = 462 x 1 + 290

Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 290 and 462, to get

462 = 290 x 1 + 172

Step 3: We consider the new divisor 290 and the new remainder 172, and apply the division lemma to get

290 = 172 x 1 + 118

We consider the new divisor 172 and the new remainder 118,and apply the division lemma to get

172 = 118 x 1 + 54

We consider the new divisor 118 and the new remainder 54,and apply the division lemma to get

118 = 54 x 2 + 10

We consider the new divisor 54 and the new remainder 10,and apply the division lemma to get

54 = 10 x 5 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 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 462 and 752 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(54,10) = HCF(118,54) = HCF(172,118) = HCF(290,172) = HCF(462,290) = HCF(752,462) .

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

Step 1: Since 431 > 2, we apply the division lemma to 431 and 2, to get

431 = 2 x 215 + 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 431 is 1

Notice that 1 = HCF(2,1) = HCF(431,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 462, 752, 431 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 462, 752, 431?

Answer: HCF of 462, 752, 431 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 462, 752, 431 using Euclid's Algorithm?

Answer: For arbitrary numbers 462, 752, 431 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.