Highest Common Factor of 242, 474, 315 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 242, 474, 315 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 242, 474, 315 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 242, 474, 315 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 242, 474, 315 is 1.

HCF(242, 474, 315) = 1

HCF of 242, 474, 315 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 242, 474, 315 is 1.

Highest Common Factor of 242,474,315 using Euclid's algorithm

Highest Common Factor of 242,474,315 is 1

Step 1: Since 474 > 242, we apply the division lemma to 474 and 242, to get

474 = 242 x 1 + 232

Step 2: Since the reminder 242 ≠ 0, we apply division lemma to 232 and 242, to get

242 = 232 x 1 + 10

Step 3: We consider the new divisor 232 and the new remainder 10, and apply the division lemma to get

232 = 10 x 23 + 2

We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 242 and 474 is 2

Notice that 2 = HCF(10,2) = HCF(232,10) = HCF(242,232) = HCF(474,242) .

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

Step 1: Since 315 > 2, we apply the division lemma to 315 and 2, to get

315 = 2 x 157 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 315 is 1

Notice that 1 = HCF(2,1) = HCF(315,2) .

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Frequently Asked Questions on HCF of 242, 474, 315 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 242, 474, 315?

Answer: HCF of 242, 474, 315 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 242, 474, 315 using Euclid's Algorithm?

Answer: For arbitrary numbers 242, 474, 315 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.