Highest Common Factor of 281, 782 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 281, 782 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 281, 782 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 281, 782 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 281, 782 is 1.

HCF(281, 782) = 1

HCF of 281, 782 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 281, 782 is 1.

Highest Common Factor of 281,782 using Euclid's algorithm

Highest Common Factor of 281,782 is 1

Step 1: Since 782 > 281, we apply the division lemma to 782 and 281, to get

782 = 281 x 2 + 220

Step 2: Since the reminder 281 ≠ 0, we apply division lemma to 220 and 281, to get

281 = 220 x 1 + 61

Step 3: We consider the new divisor 220 and the new remainder 61, and apply the division lemma to get

220 = 61 x 3 + 37

We consider the new divisor 61 and the new remainder 37,and apply the division lemma to get

61 = 37 x 1 + 24

We consider the new divisor 37 and the new remainder 24,and apply the division lemma to get

37 = 24 x 1 + 13

We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get

24 = 13 x 1 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 281 and 782 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(37,24) = HCF(61,37) = HCF(220,61) = HCF(281,220) = HCF(782,281) .

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Frequently Asked Questions on HCF of 281, 782 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 281, 782?

Answer: HCF of 281, 782 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 281, 782 using Euclid's Algorithm?

Answer: For arbitrary numbers 281, 782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.