Highest Common Factor of 645, 145, 663 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 645, 145, 663 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 645, 145, 663 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 645, 145, 663 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 645, 145, 663 is 1.

HCF(645, 145, 663) = 1

HCF of 645, 145, 663 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 645, 145, 663 is 1.

Highest Common Factor of 645,145,663 using Euclid's algorithm

Highest Common Factor of 645,145,663 is 1

Step 1: Since 645 > 145, we apply the division lemma to 645 and 145, to get

645 = 145 x 4 + 65

Step 2: Since the reminder 145 ≠ 0, we apply division lemma to 65 and 145, to get

145 = 65 x 2 + 15

Step 3: We consider the new divisor 65 and the new remainder 15, and apply the division lemma to get

65 = 15 x 4 + 5

We consider the new divisor 15 and the new remainder 5, and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 645 and 145 is 5

Notice that 5 = HCF(15,5) = HCF(65,15) = HCF(145,65) = HCF(645,145) .

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

Step 1: Since 663 > 5, we apply the division lemma to 663 and 5, to get

663 = 5 x 132 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 663 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(663,5) .

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Frequently Asked Questions on HCF of 645, 145, 663 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 645, 145, 663?

Answer: HCF of 645, 145, 663 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 645, 145, 663 using Euclid's Algorithm?

Answer: For arbitrary numbers 645, 145, 663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.