Highest Common Factor of 874, 2783, 7136 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 874, 2783, 7136 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 874, 2783, 7136 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 874, 2783, 7136 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 874, 2783, 7136 is 1.

HCF(874, 2783, 7136) = 1

HCF of 874, 2783, 7136 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 874, 2783, 7136 is 1.

Highest Common Factor of 874,2783,7136 using Euclid's algorithm

Highest Common Factor of 874,2783,7136 is 1

Step 1: Since 2783 > 874, we apply the division lemma to 2783 and 874, to get

2783 = 874 x 3 + 161

Step 2: Since the reminder 874 ≠ 0, we apply division lemma to 161 and 874, to get

874 = 161 x 5 + 69

Step 3: We consider the new divisor 161 and the new remainder 69, and apply the division lemma to get

161 = 69 x 2 + 23

We consider the new divisor 69 and the new remainder 23, and apply the division lemma to get

69 = 23 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 874 and 2783 is 23

Notice that 23 = HCF(69,23) = HCF(161,69) = HCF(874,161) = HCF(2783,874) .

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

Step 1: Since 7136 > 23, we apply the division lemma to 7136 and 23, to get

7136 = 23 x 310 + 6

Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 6 and 23, to get

23 = 6 x 3 + 5

Step 3: We consider the new divisor 6 and the new remainder 5, and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 23 and 7136 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(7136,23) .

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Frequently Asked Questions on HCF of 874, 2783, 7136 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 874, 2783, 7136?

Answer: HCF of 874, 2783, 7136 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 874, 2783, 7136 using Euclid's Algorithm?

Answer: For arbitrary numbers 874, 2783, 7136 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.