Highest Common Factor of 702, 1922, 2913 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 702, 1922, 2913 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 702, 1922, 2913 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 702, 1922, 2913 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 702, 1922, 2913 is 1.

HCF(702, 1922, 2913) = 1

HCF of 702, 1922, 2913 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 702, 1922, 2913 is 1.

Highest Common Factor of 702,1922,2913 using Euclid's algorithm

Highest Common Factor of 702,1922,2913 is 1

Step 1: Since 1922 > 702, we apply the division lemma to 1922 and 702, to get

1922 = 702 x 2 + 518

Step 2: Since the reminder 702 ≠ 0, we apply division lemma to 518 and 702, to get

702 = 518 x 1 + 184

Step 3: We consider the new divisor 518 and the new remainder 184, and apply the division lemma to get

518 = 184 x 2 + 150

We consider the new divisor 184 and the new remainder 150,and apply the division lemma to get

184 = 150 x 1 + 34

We consider the new divisor 150 and the new remainder 34,and apply the division lemma to get

150 = 34 x 4 + 14

We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get

34 = 14 x 2 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 702 and 1922 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(150,34) = HCF(184,150) = HCF(518,184) = HCF(702,518) = HCF(1922,702) .

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

Step 1: Since 2913 > 2, we apply the division lemma to 2913 and 2, to get

2913 = 2 x 1456 + 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 2913 is 1

Notice that 1 = HCF(2,1) = HCF(2913,2) .

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Frequently Asked Questions on HCF of 702, 1922, 2913 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 702, 1922, 2913?

Answer: HCF of 702, 1922, 2913 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 702, 1922, 2913 using Euclid's Algorithm?

Answer: For arbitrary numbers 702, 1922, 2913 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.