Highest Common Factor of 903, 252, 22 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 903, 252, 22 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 903, 252, 22 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 903, 252, 22 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 903, 252, 22 is 1.

HCF(903, 252, 22) = 1

HCF of 903, 252, 22 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 903, 252, 22 is 1.

Highest Common Factor of 903,252,22 using Euclid's algorithm

Highest Common Factor of 903,252,22 is 1

Step 1: Since 903 > 252, we apply the division lemma to 903 and 252, to get

903 = 252 x 3 + 147

Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 147 and 252, to get

252 = 147 x 1 + 105

Step 3: We consider the new divisor 147 and the new remainder 105, and apply the division lemma to get

147 = 105 x 1 + 42

We consider the new divisor 105 and the new remainder 42,and apply the division lemma to get

105 = 42 x 2 + 21

We consider the new divisor 42 and the new remainder 21,and apply the division lemma to get

42 = 21 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 903 and 252 is 21

Notice that 21 = HCF(42,21) = HCF(105,42) = HCF(147,105) = HCF(252,147) = HCF(903,252) .

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

Step 1: Since 22 > 21, we apply the division lemma to 22 and 21, to get

22 = 21 x 1 + 1

Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 1 and 21, to get

21 = 1 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 22 is 1

Notice that 1 = HCF(21,1) = HCF(22,21) .

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Frequently Asked Questions on HCF of 903, 252, 22 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 903, 252, 22?

Answer: HCF of 903, 252, 22 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 903, 252, 22 using Euclid's Algorithm?

Answer: For arbitrary numbers 903, 252, 22 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.