Highest Common Factor of 561, 912, 625 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 561, 912, 625 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 561, 912, 625 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 561, 912, 625 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 561, 912, 625 is 1.

HCF(561, 912, 625) = 1

HCF of 561, 912, 625 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 561, 912, 625 is 1.

Highest Common Factor of 561,912,625 using Euclid's algorithm

Highest Common Factor of 561,912,625 is 1

Step 1: Since 912 > 561, we apply the division lemma to 912 and 561, to get

912 = 561 x 1 + 351

Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 351 and 561, to get

561 = 351 x 1 + 210

Step 3: We consider the new divisor 351 and the new remainder 210, and apply the division lemma to get

351 = 210 x 1 + 141

We consider the new divisor 210 and the new remainder 141,and apply the division lemma to get

210 = 141 x 1 + 69

We consider the new divisor 141 and the new remainder 69,and apply the division lemma to get

141 = 69 x 2 + 3

We consider the new divisor 69 and the new remainder 3,and apply the division lemma to get

69 = 3 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 561 and 912 is 3

Notice that 3 = HCF(69,3) = HCF(141,69) = HCF(210,141) = HCF(351,210) = HCF(561,351) = HCF(912,561) .

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

Step 1: Since 625 > 3, we apply the division lemma to 625 and 3, to get

625 = 3 x 208 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 625 is 1

Notice that 1 = HCF(3,1) = HCF(625,3) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 561, 912, 625 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 561, 912, 625?

Answer: HCF of 561, 912, 625 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 561, 912, 625 using Euclid's Algorithm?

Answer: For arbitrary numbers 561, 912, 625 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.