Highest Common Factor of 791, 500, 998 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 791, 500, 998 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 791, 500, 998 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 791, 500, 998 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 791, 500, 998 is 1.

HCF(791, 500, 998) = 1

HCF of 791, 500, 998 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 791, 500, 998 is 1.

Highest Common Factor of 791,500,998 using Euclid's algorithm

Highest Common Factor of 791,500,998 is 1

Step 1: Since 791 > 500, we apply the division lemma to 791 and 500, to get

791 = 500 x 1 + 291

Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 291 and 500, to get

500 = 291 x 1 + 209

Step 3: We consider the new divisor 291 and the new remainder 209, and apply the division lemma to get

291 = 209 x 1 + 82

We consider the new divisor 209 and the new remainder 82,and apply the division lemma to get

209 = 82 x 2 + 45

We consider the new divisor 82 and the new remainder 45,and apply the division lemma to get

82 = 45 x 1 + 37

We consider the new divisor 45 and the new remainder 37,and apply the division lemma to get

45 = 37 x 1 + 8

We consider the new divisor 37 and the new remainder 8,and apply the division lemma to get

37 = 8 x 4 + 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 791 and 500 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(37,8) = HCF(45,37) = HCF(82,45) = HCF(209,82) = HCF(291,209) = HCF(500,291) = HCF(791,500) .

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

Step 1: Since 998 > 1, we apply the division lemma to 998 and 1, to get

998 = 1 x 998 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 998 is 1

Notice that 1 = HCF(998,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 791, 500, 998 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 791, 500, 998?

Answer: HCF of 791, 500, 998 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 791, 500, 998 using Euclid's Algorithm?

Answer: For arbitrary numbers 791, 500, 998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.