Highest Common Factor of 741, 474, 186 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 741, 474, 186 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 741, 474, 186 is 3 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 741, 474, 186 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 741, 474, 186 is 3.

HCF(741, 474, 186) = 3

HCF of 741, 474, 186 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 741, 474, 186 is 3.

Highest Common Factor of 741,474,186 using Euclid's algorithm

Highest Common Factor of 741,474,186 is 3

Step 1: Since 741 > 474, we apply the division lemma to 741 and 474, to get

741 = 474 x 1 + 267

Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 267 and 474, to get

474 = 267 x 1 + 207

Step 3: We consider the new divisor 267 and the new remainder 207, and apply the division lemma to get

267 = 207 x 1 + 60

We consider the new divisor 207 and the new remainder 60,and apply the division lemma to get

207 = 60 x 3 + 27

We consider the new divisor 60 and the new remainder 27,and apply the division lemma to get

60 = 27 x 2 + 6

We consider the new divisor 27 and the new remainder 6,and apply the division lemma to get

27 = 6 x 4 + 3

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

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 741 and 474 is 3

Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(60,27) = HCF(207,60) = HCF(267,207) = HCF(474,267) = HCF(741,474) .

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

Step 1: Since 186 > 3, we apply the division lemma to 186 and 3, to get

186 = 3 x 62 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 186 is 3

Notice that 3 = HCF(186,3) .

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Frequently Asked Questions on HCF of 741, 474, 186 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 741, 474, 186?

Answer: HCF of 741, 474, 186 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 741, 474, 186 using Euclid's Algorithm?

Answer: For arbitrary numbers 741, 474, 186 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.