Highest Common Factor of 409, 656, 496 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 409, 656, 496 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 409, 656, 496 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 409, 656, 496 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 409, 656, 496 is 1.

HCF(409, 656, 496) = 1

HCF of 409, 656, 496 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 409, 656, 496 is 1.

Highest Common Factor of 409,656,496 using Euclid's algorithm

Highest Common Factor of 409,656,496 is 1

Step 1: Since 656 > 409, we apply the division lemma to 656 and 409, to get

656 = 409 x 1 + 247

Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 247 and 409, to get

409 = 247 x 1 + 162

Step 3: We consider the new divisor 247 and the new remainder 162, and apply the division lemma to get

247 = 162 x 1 + 85

We consider the new divisor 162 and the new remainder 85,and apply the division lemma to get

162 = 85 x 1 + 77

We consider the new divisor 85 and the new remainder 77,and apply the division lemma to get

85 = 77 x 1 + 8

We consider the new divisor 77 and the new remainder 8,and apply the division lemma to get

77 = 8 x 9 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

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 409 and 656 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(77,8) = HCF(85,77) = HCF(162,85) = HCF(247,162) = HCF(409,247) = HCF(656,409) .

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

Step 1: Since 496 > 1, we apply the division lemma to 496 and 1, to get

496 = 1 x 496 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 496 is 1

Notice that 1 = HCF(496,1) .

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Frequently Asked Questions on HCF of 409, 656, 496 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 409, 656, 496?

Answer: HCF of 409, 656, 496 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 409, 656, 496 using Euclid's Algorithm?

Answer: For arbitrary numbers 409, 656, 496 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.