Highest Common Factor of 402, 717, 379 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 402, 717, 379 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 402, 717, 379 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 402, 717, 379 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 402, 717, 379 is 1.

HCF(402, 717, 379) = 1

HCF of 402, 717, 379 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 402, 717, 379 is 1.

Highest Common Factor of 402,717,379 using Euclid's algorithm

Highest Common Factor of 402,717,379 is 1

Step 1: Since 717 > 402, we apply the division lemma to 717 and 402, to get

717 = 402 x 1 + 315

Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 315 and 402, to get

402 = 315 x 1 + 87

Step 3: We consider the new divisor 315 and the new remainder 87, and apply the division lemma to get

315 = 87 x 3 + 54

We consider the new divisor 87 and the new remainder 54,and apply the division lemma to get

87 = 54 x 1 + 33

We consider the new divisor 54 and the new remainder 33,and apply the division lemma to get

54 = 33 x 1 + 21

We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get

33 = 21 x 1 + 12

We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get

21 = 12 x 1 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 402 and 717 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(54,33) = HCF(87,54) = HCF(315,87) = HCF(402,315) = HCF(717,402) .

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

Step 1: Since 379 > 3, we apply the division lemma to 379 and 3, to get

379 = 3 x 126 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 379 is 1

Notice that 1 = HCF(3,1) = HCF(379,3) .

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Frequently Asked Questions on HCF of 402, 717, 379 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 402, 717, 379?

Answer: HCF of 402, 717, 379 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 402, 717, 379 using Euclid's Algorithm?

Answer: For arbitrary numbers 402, 717, 379 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.