Highest Common Factor of 500, 844, 782 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 500, 844, 782 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 500, 844, 782 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 500, 844, 782 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 500, 844, 782 is 2.

HCF(500, 844, 782) = 2

HCF of 500, 844, 782 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 500, 844, 782 is 2.

Highest Common Factor of 500,844,782 using Euclid's algorithm

Highest Common Factor of 500,844,782 is 2

Step 1: Since 844 > 500, we apply the division lemma to 844 and 500, to get

844 = 500 x 1 + 344

Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 344 and 500, to get

500 = 344 x 1 + 156

Step 3: We consider the new divisor 344 and the new remainder 156, and apply the division lemma to get

344 = 156 x 2 + 32

We consider the new divisor 156 and the new remainder 32,and apply the division lemma to get

156 = 32 x 4 + 28

We consider the new divisor 32 and the new remainder 28,and apply the division lemma to get

32 = 28 x 1 + 4

We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get

28 = 4 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 500 and 844 is 4

Notice that 4 = HCF(28,4) = HCF(32,28) = HCF(156,32) = HCF(344,156) = HCF(500,344) = HCF(844,500) .

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

Step 1: Since 782 > 4, we apply the division lemma to 782 and 4, to get

782 = 4 x 195 + 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 782 is 2

Notice that 2 = HCF(4,2) = HCF(782,4) .

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Frequently Asked Questions on HCF of 500, 844, 782 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 500, 844, 782?

Answer: HCF of 500, 844, 782 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 500, 844, 782 using Euclid's Algorithm?

Answer: For arbitrary numbers 500, 844, 782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.