Highest Common Factor of 993, 607, 18 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 993, 607, 18 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 993, 607, 18 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 993, 607, 18 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 993, 607, 18 is 1.

HCF(993, 607, 18) = 1

HCF of 993, 607, 18 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 993, 607, 18 is 1.

Highest Common Factor of 993,607,18 using Euclid's algorithm

Highest Common Factor of 993,607,18 is 1

Step 1: Since 993 > 607, we apply the division lemma to 993 and 607, to get

993 = 607 x 1 + 386

Step 2: Since the reminder 607 ≠ 0, we apply division lemma to 386 and 607, to get

607 = 386 x 1 + 221

Step 3: We consider the new divisor 386 and the new remainder 221, and apply the division lemma to get

386 = 221 x 1 + 165

We consider the new divisor 221 and the new remainder 165,and apply the division lemma to get

221 = 165 x 1 + 56

We consider the new divisor 165 and the new remainder 56,and apply the division lemma to get

165 = 56 x 2 + 53

We consider the new divisor 56 and the new remainder 53,and apply the division lemma to get

56 = 53 x 1 + 3

We consider the new divisor 53 and the new remainder 3,and apply the division lemma to get

53 = 3 x 17 + 2

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

3 = 2 x 1 + 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 993 and 607 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(53,3) = HCF(56,53) = HCF(165,56) = HCF(221,165) = HCF(386,221) = HCF(607,386) = HCF(993,607) .

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

Step 1: Since 18 > 1, we apply the division lemma to 18 and 1, to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 18 is 1

Notice that 1 = HCF(18,1) .

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Frequently Asked Questions on HCF of 993, 607, 18 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 993, 607, 18?

Answer: HCF of 993, 607, 18 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 993, 607, 18 using Euclid's Algorithm?

Answer: For arbitrary numbers 993, 607, 18 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.