Highest Common Factor of 240, 421, 364 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 240, 421, 364 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 240, 421, 364 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 240, 421, 364 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 240, 421, 364 is 1.

HCF(240, 421, 364) = 1

HCF of 240, 421, 364 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 240, 421, 364 is 1.

Highest Common Factor of 240,421,364 using Euclid's algorithm

Highest Common Factor of 240,421,364 is 1

Step 1: Since 421 > 240, we apply the division lemma to 421 and 240, to get

421 = 240 x 1 + 181

Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 181 and 240, to get

240 = 181 x 1 + 59

Step 3: We consider the new divisor 181 and the new remainder 59, and apply the division lemma to get

181 = 59 x 3 + 4

We consider the new divisor 59 and the new remainder 4,and apply the division lemma to get

59 = 4 x 14 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 240 and 421 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(59,4) = HCF(181,59) = HCF(240,181) = HCF(421,240) .

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

Step 1: Since 364 > 1, we apply the division lemma to 364 and 1, to get

364 = 1 x 364 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 364 is 1

Notice that 1 = HCF(364,1) .

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Frequently Asked Questions on HCF of 240, 421, 364 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 240, 421, 364?

Answer: HCF of 240, 421, 364 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 240, 421, 364 using Euclid's Algorithm?

Answer: For arbitrary numbers 240, 421, 364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.