Highest Common Factor of 781, 414 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 781, 414 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 781, 414 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 781, 414 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 781, 414 is 1.

HCF(781, 414) = 1

HCF of 781, 414 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 781, 414 is 1.

Highest Common Factor of 781,414 using Euclid's algorithm

Highest Common Factor of 781,414 is 1

Step 1: Since 781 > 414, we apply the division lemma to 781 and 414, to get

781 = 414 x 1 + 367

Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 367 and 414, to get

414 = 367 x 1 + 47

Step 3: We consider the new divisor 367 and the new remainder 47, and apply the division lemma to get

367 = 47 x 7 + 38

We consider the new divisor 47 and the new remainder 38,and apply the division lemma to get

47 = 38 x 1 + 9

We consider the new divisor 38 and the new remainder 9,and apply the division lemma to get

38 = 9 x 4 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 781 and 414 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(38,9) = HCF(47,38) = HCF(367,47) = HCF(414,367) = HCF(781,414) .

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Frequently Asked Questions on HCF of 781, 414 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 781, 414?

Answer: HCF of 781, 414 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 781, 414 using Euclid's Algorithm?

Answer: For arbitrary numbers 781, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.