Highest Common Factor of 402, 663, 842 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, 663, 842 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 402, 663, 842 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, 663, 842 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, 663, 842 is 1.

HCF(402, 663, 842) = 1

HCF of 402, 663, 842 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, 663, 842 is 1.

Highest Common Factor of 402,663,842 using Euclid's algorithm

Highest Common Factor of 402,663,842 is 1

Step 1: Since 663 > 402, we apply the division lemma to 663 and 402, to get

663 = 402 x 1 + 261

Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 261 and 402, to get

402 = 261 x 1 + 141

Step 3: We consider the new divisor 261 and the new remainder 141, and apply the division lemma to get

261 = 141 x 1 + 120

We consider the new divisor 141 and the new remainder 120,and apply the division lemma to get

141 = 120 x 1 + 21

We consider the new divisor 120 and the new remainder 21,and apply the division lemma to get

120 = 21 x 5 + 15

We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get

21 = 15 x 1 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 402 and 663 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(120,21) = HCF(141,120) = HCF(261,141) = HCF(402,261) = HCF(663,402) .

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

Step 1: Since 842 > 3, we apply the division lemma to 842 and 3, to get

842 = 3 x 280 + 2

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

3 = 2 x 1 + 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 3 and 842 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(842,3) .

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Frequently Asked Questions on HCF of 402, 663, 842 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, 663, 842?

Answer: HCF of 402, 663, 842 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 402, 663, 842 using Euclid's Algorithm?

Answer: For arbitrary numbers 402, 663, 842 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.