Highest Common Factor of 496, 324, 802 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 496, 324, 802 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 496, 324, 802 is 2 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 496, 324, 802 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 496, 324, 802 is 2.

HCF(496, 324, 802) = 2

HCF of 496, 324, 802 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 496, 324, 802 is 2.

Highest Common Factor of 496,324,802 using Euclid's algorithm

Highest Common Factor of 496,324,802 is 2

Step 1: Since 496 > 324, we apply the division lemma to 496 and 324, to get

496 = 324 x 1 + 172

Step 2: Since the reminder 324 ≠ 0, we apply division lemma to 172 and 324, to get

324 = 172 x 1 + 152

Step 3: We consider the new divisor 172 and the new remainder 152, and apply the division lemma to get

172 = 152 x 1 + 20

We consider the new divisor 152 and the new remainder 20,and apply the division lemma to get

152 = 20 x 7 + 12

We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get

20 = 12 x 1 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 496 and 324 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(152,20) = HCF(172,152) = HCF(324,172) = HCF(496,324) .

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

Step 1: Since 802 > 4, we apply the division lemma to 802 and 4, to get

802 = 4 x 200 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 802 is 2

Notice that 2 = HCF(4,2) = HCF(802,4) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 496, 324, 802 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 496, 324, 802?

Answer: HCF of 496, 324, 802 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 496, 324, 802 using Euclid's Algorithm?

Answer: For arbitrary numbers 496, 324, 802 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.