Highest Common Factor of 424, 265, 320 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 424, 265, 320 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 424, 265, 320 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 424, 265, 320 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 424, 265, 320 is 1.

HCF(424, 265, 320) = 1

HCF of 424, 265, 320 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 424, 265, 320 is 1.

Highest Common Factor of 424,265,320 using Euclid's algorithm

Highest Common Factor of 424,265,320 is 1

Step 1: Since 424 > 265, we apply the division lemma to 424 and 265, to get

424 = 265 x 1 + 159

Step 2: Since the reminder 265 ≠ 0, we apply division lemma to 159 and 265, to get

265 = 159 x 1 + 106

Step 3: We consider the new divisor 159 and the new remainder 106, and apply the division lemma to get

159 = 106 x 1 + 53

We consider the new divisor 106 and the new remainder 53, and apply the division lemma to get

106 = 53 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 53, the HCF of 424 and 265 is 53

Notice that 53 = HCF(106,53) = HCF(159,106) = HCF(265,159) = HCF(424,265) .

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

Step 1: Since 320 > 53, we apply the division lemma to 320 and 53, to get

320 = 53 x 6 + 2

Step 2: Since the reminder 53 ≠ 0, we apply division lemma to 2 and 53, to get

53 = 2 x 26 + 1

Step 3: 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 53 and 320 is 1

Notice that 1 = HCF(2,1) = HCF(53,2) = HCF(320,53) .

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Frequently Asked Questions on HCF of 424, 265, 320 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 424, 265, 320?

Answer: HCF of 424, 265, 320 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 424, 265, 320 using Euclid's Algorithm?

Answer: For arbitrary numbers 424, 265, 320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.