Highest Common Factor of 252, 905, 242 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, 905, 242 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 252, 905, 242 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, 905, 242 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, 905, 242 is 1.

HCF(252, 905, 242) = 1

HCF of 252, 905, 242 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, 905, 242 is 1.

Highest Common Factor of 252,905,242 using Euclid's algorithm

Highest Common Factor of 252,905,242 is 1

Step 1: Since 905 > 252, we apply the division lemma to 905 and 252, to get

905 = 252 x 3 + 149

Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 149 and 252, to get

252 = 149 x 1 + 103

Step 3: We consider the new divisor 149 and the new remainder 103, and apply the division lemma to get

149 = 103 x 1 + 46

We consider the new divisor 103 and the new remainder 46,and apply the division lemma to get

103 = 46 x 2 + 11

We consider the new divisor 46 and the new remainder 11,and apply the division lemma to get

46 = 11 x 4 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 905 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(46,11) = HCF(103,46) = HCF(149,103) = HCF(252,149) = HCF(905,252) .

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

Step 1: Since 242 > 1, we apply the division lemma to 242 and 1, to get

242 = 1 x 242 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 242 is 1

Notice that 1 = HCF(242,1) .

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Frequently Asked Questions on HCF of 252, 905, 242 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, 905, 242?

Answer: HCF of 252, 905, 242 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 252, 905, 242 using Euclid's Algorithm?

Answer: For arbitrary numbers 252, 905, 242 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.