Highest Common Factor of 754, 156, 561 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 754, 156, 561 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 754, 156, 561 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 754, 156, 561 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 754, 156, 561 is 1.

HCF(754, 156, 561) = 1

HCF of 754, 156, 561 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 754, 156, 561 is 1.

Highest Common Factor of 754,156,561 using Euclid's algorithm

Highest Common Factor of 754,156,561 is 1

Step 1: Since 754 > 156, we apply the division lemma to 754 and 156, to get

754 = 156 x 4 + 130

Step 2: Since the reminder 156 ≠ 0, we apply division lemma to 130 and 156, to get

156 = 130 x 1 + 26

Step 3: We consider the new divisor 130 and the new remainder 26, and apply the division lemma to get

130 = 26 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 754 and 156 is 26

Notice that 26 = HCF(130,26) = HCF(156,130) = HCF(754,156) .

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

Step 1: Since 561 > 26, we apply the division lemma to 561 and 26, to get

561 = 26 x 21 + 15

Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 15 and 26, to get

26 = 15 x 1 + 11

Step 3: We consider the new divisor 15 and the new remainder 11, and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 26 and 561 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(561,26) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 754, 156, 561 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 754, 156, 561?

Answer: HCF of 754, 156, 561 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 754, 156, 561 using Euclid's Algorithm?

Answer: For arbitrary numbers 754, 156, 561 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.