Highest Common Factor of 393, 963, 68 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, 963, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 393, 963, 68 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, 963, 68 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, 963, 68 is 1.

HCF(393, 963, 68) = 1

HCF of 393, 963, 68 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, 963, 68 is 1.

Highest Common Factor of 393,963,68 using Euclid's algorithm

Highest Common Factor of 393,963,68 is 1

Step 1: Since 963 > 393, we apply the division lemma to 963 and 393, to get

963 = 393 x 2 + 177

Step 2: Since the reminder 393 ≠ 0, we apply division lemma to 177 and 393, to get

393 = 177 x 2 + 39

Step 3: We consider the new divisor 177 and the new remainder 39, and apply the division lemma to get

177 = 39 x 4 + 21

We consider the new divisor 39 and the new remainder 21,and apply the division lemma to get

39 = 21 x 1 + 18

We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get

21 = 18 x 1 + 3

We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get

18 = 3 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 393 and 963 is 3

Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(39,21) = HCF(177,39) = HCF(393,177) = HCF(963,393) .

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

Step 1: Since 68 > 3, we apply the division lemma to 68 and 3, to get

68 = 3 x 22 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 68 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(68,3) .

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Frequently Asked Questions on HCF of 393, 963, 68 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, 963, 68?

Answer: HCF of 393, 963, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 393, 963, 68 using Euclid's Algorithm?

Answer: For arbitrary numbers 393, 963, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.