Highest Common Factor of 393, 666, 874 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 393, 666, 874 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 393, 666, 874 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 393, 666, 874 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 393, 666, 874 is 1.

HCF(393, 666, 874) = 1

HCF of 393, 666, 874 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 393, 666, 874 is 1.

Highest Common Factor of 393,666,874 using Euclid's algorithm

Highest Common Factor of 393,666,874 is 1

Step 1: Since 666 > 393, we apply the division lemma to 666 and 393, to get

666 = 393 x 1 + 273

Step 2: Since the reminder 393 ≠ 0, we apply division lemma to 273 and 393, to get

393 = 273 x 1 + 120

Step 3: We consider the new divisor 273 and the new remainder 120, and apply the division lemma to get

273 = 120 x 2 + 33

We consider the new divisor 120 and the new remainder 33,and apply the division lemma to get

120 = 33 x 3 + 21

We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get

33 = 21 x 1 + 12

We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get

21 = 12 x 1 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 393 and 666 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(120,33) = HCF(273,120) = HCF(393,273) = HCF(666,393) .

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

Step 1: Since 874 > 3, we apply the division lemma to 874 and 3, to get

874 = 3 x 291 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 874 is 1

Notice that 1 = HCF(3,1) = HCF(874,3) .

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Frequently Asked Questions on HCF of 393, 666, 874 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 393, 666, 874?

Answer: HCF of 393, 666, 874 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 393, 666, 874 using Euclid's Algorithm?

Answer: For arbitrary numbers 393, 666, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.