Highest Common Factor of 456, 591 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 456, 591 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 456, 591 is 3 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 456, 591 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 456, 591 is 3.

HCF(456, 591) = 3

HCF of 456, 591 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 456, 591 is 3.

Highest Common Factor of 456,591 using Euclid's algorithm

Highest Common Factor of 456,591 is 3

Step 1: Since 591 > 456, we apply the division lemma to 591 and 456, to get

591 = 456 x 1 + 135

Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 135 and 456, to get

456 = 135 x 3 + 51

Step 3: We consider the new divisor 135 and the new remainder 51, and apply the division lemma to get

135 = 51 x 2 + 33

We consider the new divisor 51 and the new remainder 33,and apply the division lemma to get

51 = 33 x 1 + 18

We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get

33 = 18 x 1 + 15

We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get

18 = 15 x 1 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 456 and 591 is 3

Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(51,33) = HCF(135,51) = HCF(456,135) = HCF(591,456) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 456, 591 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 456, 591?

Answer: HCF of 456, 591 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 456, 591 using Euclid's Algorithm?

Answer: For arbitrary numbers 456, 591 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.