Highest Common Factor of 381, 602, 490 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 381, 602, 490 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 381, 602, 490 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 381, 602, 490 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 381, 602, 490 is 1.

HCF(381, 602, 490) = 1

HCF of 381, 602, 490 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 381, 602, 490 is 1.

Highest Common Factor of 381,602,490 using Euclid's algorithm

Highest Common Factor of 381,602,490 is 1

Step 1: Since 602 > 381, we apply the division lemma to 602 and 381, to get

602 = 381 x 1 + 221

Step 2: Since the reminder 381 ≠ 0, we apply division lemma to 221 and 381, to get

381 = 221 x 1 + 160

Step 3: We consider the new divisor 221 and the new remainder 160, and apply the division lemma to get

221 = 160 x 1 + 61

We consider the new divisor 160 and the new remainder 61,and apply the division lemma to get

160 = 61 x 2 + 38

We consider the new divisor 61 and the new remainder 38,and apply the division lemma to get

61 = 38 x 1 + 23

We consider the new divisor 38 and the new remainder 23,and apply the division lemma to get

38 = 23 x 1 + 15

We consider the new divisor 23 and the new remainder 15,and apply the division lemma to get

23 = 15 x 1 + 8

We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get

15 = 8 x 1 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 381 and 602 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(23,15) = HCF(38,23) = HCF(61,38) = HCF(160,61) = HCF(221,160) = HCF(381,221) = HCF(602,381) .

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

Step 1: Since 490 > 1, we apply the division lemma to 490 and 1, to get

490 = 1 x 490 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 490 is 1

Notice that 1 = HCF(490,1) .

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Frequently Asked Questions on HCF of 381, 602, 490 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 381, 602, 490?

Answer: HCF of 381, 602, 490 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 381, 602, 490 using Euclid's Algorithm?

Answer: For arbitrary numbers 381, 602, 490 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.