Highest Common Factor of 57, 93, 53, 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 57, 93, 53, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 57, 93, 53, 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 57, 93, 53, 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 57, 93, 53, 68 is 1.

HCF(57, 93, 53, 68) = 1

HCF of 57, 93, 53, 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 57, 93, 53, 68 is 1.

Highest Common Factor of 57,93,53,68 using Euclid's algorithm

Highest Common Factor of 57,93,53,68 is 1

Step 1: Since 93 > 57, we apply the division lemma to 93 and 57, to get

93 = 57 x 1 + 36

Step 2: Since the reminder 57 ≠ 0, we apply division lemma to 36 and 57, to get

57 = 36 x 1 + 21

Step 3: We consider the new divisor 36 and the new remainder 21, and apply the division lemma to get

36 = 21 x 1 + 15

We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get

21 = 15 x 1 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 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 57 and 93 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(57,36) = HCF(93,57) .

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

Step 1: Since 53 > 3, we apply the division lemma to 53 and 3, to get

53 = 3 x 17 + 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 53 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(53,3) .

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

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

68 = 1 x 68 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68 is 1

Notice that 1 = HCF(68,1) .

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Frequently Asked Questions on HCF of 57, 93, 53, 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 57, 93, 53, 68?

Answer: HCF of 57, 93, 53, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 57, 93, 53, 68 using Euclid's Algorithm?

Answer: For arbitrary numbers 57, 93, 53, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.