Highest Common Factor of 490, 792, 909 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, 792, 909 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 490, 792, 909 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, 792, 909 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, 792, 909 is 1.

HCF(490, 792, 909) = 1

HCF of 490, 792, 909 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, 792, 909 is 1.

Highest Common Factor of 490,792,909 using Euclid's algorithm

Highest Common Factor of 490,792,909 is 1

Step 1: Since 792 > 490, we apply the division lemma to 792 and 490, to get

792 = 490 x 1 + 302

Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 302 and 490, to get

490 = 302 x 1 + 188

Step 3: We consider the new divisor 302 and the new remainder 188, and apply the division lemma to get

302 = 188 x 1 + 114

We consider the new divisor 188 and the new remainder 114,and apply the division lemma to get

188 = 114 x 1 + 74

We consider the new divisor 114 and the new remainder 74,and apply the division lemma to get

114 = 74 x 1 + 40

We consider the new divisor 74 and the new remainder 40,and apply the division lemma to get

74 = 40 x 1 + 34

We consider the new divisor 40 and the new remainder 34,and apply the division lemma to get

40 = 34 x 1 + 6

We consider the new divisor 34 and the new remainder 6,and apply the division lemma to get

34 = 6 x 5 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 490 and 792 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(34,6) = HCF(40,34) = HCF(74,40) = HCF(114,74) = HCF(188,114) = HCF(302,188) = HCF(490,302) = HCF(792,490) .

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

Step 1: Since 909 > 2, we apply the division lemma to 909 and 2, to get

909 = 2 x 454 + 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 909 is 1

Notice that 1 = HCF(2,1) = HCF(909,2) .

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Frequently Asked Questions on HCF of 490, 792, 909 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, 792, 909?

Answer: HCF of 490, 792, 909 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 490, 792, 909 using Euclid's Algorithm?

Answer: For arbitrary numbers 490, 792, 909 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.