Highest Common Factor of 751, 420, 497 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 751, 420, 497 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 751, 420, 497 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 751, 420, 497 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 751, 420, 497 is 1.

HCF(751, 420, 497) = 1

HCF of 751, 420, 497 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 751, 420, 497 is 1.

Highest Common Factor of 751,420,497 using Euclid's algorithm

Highest Common Factor of 751,420,497 is 1

Step 1: Since 751 > 420, we apply the division lemma to 751 and 420, to get

751 = 420 x 1 + 331

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 331 and 420, to get

420 = 331 x 1 + 89

Step 3: We consider the new divisor 331 and the new remainder 89, and apply the division lemma to get

331 = 89 x 3 + 64

We consider the new divisor 89 and the new remainder 64,and apply the division lemma to get

89 = 64 x 1 + 25

We consider the new divisor 64 and the new remainder 25,and apply the division lemma to get

64 = 25 x 2 + 14

We consider the new divisor 25 and the new remainder 14,and apply the division lemma to get

25 = 14 x 1 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 751 and 420 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(25,14) = HCF(64,25) = HCF(89,64) = HCF(331,89) = HCF(420,331) = HCF(751,420) .

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

Step 1: Since 497 > 1, we apply the division lemma to 497 and 1, to get

497 = 1 x 497 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 497 is 1

Notice that 1 = HCF(497,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 751, 420, 497 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 751, 420, 497?

Answer: HCF of 751, 420, 497 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 751, 420, 497 using Euclid's Algorithm?

Answer: For arbitrary numbers 751, 420, 497 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.