Highest Common Factor of 645, 456, 521 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, 456, 521 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 645, 456, 521 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, 456, 521 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, 456, 521 is 1.

HCF(645, 456, 521) = 1

HCF of 645, 456, 521 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, 456, 521 is 1.

Highest Common Factor of 645,456,521 using Euclid's algorithm

Highest Common Factor of 645,456,521 is 1

Step 1: Since 645 > 456, we apply the division lemma to 645 and 456, to get

645 = 456 x 1 + 189

Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 189 and 456, to get

456 = 189 x 2 + 78

Step 3: We consider the new divisor 189 and the new remainder 78, and apply the division lemma to get

189 = 78 x 2 + 33

We consider the new divisor 78 and the new remainder 33,and apply the division lemma to get

78 = 33 x 2 + 12

We consider the new divisor 33 and the new remainder 12,and apply the division lemma to get

33 = 12 x 2 + 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 645 and 456 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(33,12) = HCF(78,33) = HCF(189,78) = HCF(456,189) = HCF(645,456) .

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

Step 1: Since 521 > 3, we apply the division lemma to 521 and 3, to get

521 = 3 x 173 + 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 521 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(521,3) .

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Frequently Asked Questions on HCF of 645, 456, 521 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, 456, 521?

Answer: HCF of 645, 456, 521 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 645, 456, 521 using Euclid's Algorithm?

Answer: For arbitrary numbers 645, 456, 521 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.