Highest Common Factor of 490, 788, 61 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 490, 788, 61 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 490, 788, 61 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 490, 788, 61 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 490, 788, 61 is 1.

HCF(490, 788, 61) = 1

HCF of 490, 788, 61 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 490, 788, 61 is 1.

Highest Common Factor of 490,788,61 using Euclid's algorithm

Highest Common Factor of 490,788,61 is 1

Step 1: Since 788 > 490, we apply the division lemma to 788 and 490, to get

788 = 490 x 1 + 298

Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 298 and 490, to get

490 = 298 x 1 + 192

Step 3: We consider the new divisor 298 and the new remainder 192, and apply the division lemma to get

298 = 192 x 1 + 106

We consider the new divisor 192 and the new remainder 106,and apply the division lemma to get

192 = 106 x 1 + 86

We consider the new divisor 106 and the new remainder 86,and apply the division lemma to get

106 = 86 x 1 + 20

We consider the new divisor 86 and the new remainder 20,and apply the division lemma to get

86 = 20 x 4 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 490 and 788 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(86,20) = HCF(106,86) = HCF(192,106) = HCF(298,192) = HCF(490,298) = HCF(788,490) .

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

Step 1: Since 61 > 2, we apply the division lemma to 61 and 2, to get

61 = 2 x 30 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 61 is 1

Notice that 1 = HCF(2,1) = HCF(61,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 490, 788, 61 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 490, 788, 61?

Answer: HCF of 490, 788, 61 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 490, 788, 61 using Euclid's Algorithm?

Answer: For arbitrary numbers 490, 788, 61 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.