Highest Common Factor of 909, 361, 42 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 909, 361, 42 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 909, 361, 42 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 909, 361, 42 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 909, 361, 42 is 1.

HCF(909, 361, 42) = 1

HCF of 909, 361, 42 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 909, 361, 42 is 1.

Highest Common Factor of 909,361,42 using Euclid's algorithm

Highest Common Factor of 909,361,42 is 1

Step 1: Since 909 > 361, we apply the division lemma to 909 and 361, to get

909 = 361 x 2 + 187

Step 2: Since the reminder 361 ≠ 0, we apply division lemma to 187 and 361, to get

361 = 187 x 1 + 174

Step 3: We consider the new divisor 187 and the new remainder 174, and apply the division lemma to get

187 = 174 x 1 + 13

We consider the new divisor 174 and the new remainder 13,and apply the division lemma to get

174 = 13 x 13 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 909 and 361 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(174,13) = HCF(187,174) = HCF(361,187) = HCF(909,361) .

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

Step 1: Since 42 > 1, we apply the division lemma to 42 and 1, to get

42 = 1 x 42 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42 is 1

Notice that 1 = HCF(42,1) .

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Frequently Asked Questions on HCF of 909, 361, 42 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 909, 361, 42?

Answer: HCF of 909, 361, 42 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 909, 361, 42 using Euclid's Algorithm?

Answer: For arbitrary numbers 909, 361, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.