Highest Common Factor of 252, 991, 654 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 252, 991, 654 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 252, 991, 654 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 252, 991, 654 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 252, 991, 654 is 1.

HCF(252, 991, 654) = 1

HCF of 252, 991, 654 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 252, 991, 654 is 1.

Highest Common Factor of 252,991,654 using Euclid's algorithm

Highest Common Factor of 252,991,654 is 1

Step 1: Since 991 > 252, we apply the division lemma to 991 and 252, to get

991 = 252 x 3 + 235

Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 235 and 252, to get

252 = 235 x 1 + 17

Step 3: We consider the new divisor 235 and the new remainder 17, and apply the division lemma to get

235 = 17 x 13 + 14

We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get

17 = 14 x 1 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 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 252 and 991 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(235,17) = HCF(252,235) = HCF(991,252) .

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

Step 1: Since 654 > 1, we apply the division lemma to 654 and 1, to get

654 = 1 x 654 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 654 is 1

Notice that 1 = HCF(654,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 252, 991, 654 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 252, 991, 654?

Answer: HCF of 252, 991, 654 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 252, 991, 654 using Euclid's Algorithm?

Answer: For arbitrary numbers 252, 991, 654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.