Highest Common Factor of 174, 203, 781 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 174, 203, 781 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 174, 203, 781 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 174, 203, 781 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 174, 203, 781 is 1.

HCF(174, 203, 781) = 1

HCF of 174, 203, 781 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 174, 203, 781 is 1.

Highest Common Factor of 174,203,781 using Euclid's algorithm

Highest Common Factor of 174,203,781 is 1

Step 1: Since 203 > 174, we apply the division lemma to 203 and 174, to get

203 = 174 x 1 + 29

Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 29 and 174, to get

174 = 29 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 29, the HCF of 174 and 203 is 29

Notice that 29 = HCF(174,29) = HCF(203,174) .

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

Step 1: Since 781 > 29, we apply the division lemma to 781 and 29, to get

781 = 29 x 26 + 27

Step 2: Since the reminder 29 ≠ 0, we apply division lemma to 27 and 29, to get

29 = 27 x 1 + 2

Step 3: We consider the new divisor 27 and the new remainder 2, and apply the division lemma to get

27 = 2 x 13 + 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 29 and 781 is 1

Notice that 1 = HCF(2,1) = HCF(27,2) = HCF(29,27) = HCF(781,29) .

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Frequently Asked Questions on HCF of 174, 203, 781 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 174, 203, 781?

Answer: HCF of 174, 203, 781 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 174, 203, 781 using Euclid's Algorithm?

Answer: For arbitrary numbers 174, 203, 781 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.