Highest Common Factor of 645, 5522 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, 5522 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 645, 5522 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, 5522 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, 5522 is 1.

HCF(645, 5522) = 1

HCF of 645, 5522 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, 5522 is 1.

Highest Common Factor of 645,5522 using Euclid's algorithm

Highest Common Factor of 645,5522 is 1

Step 1: Since 5522 > 645, we apply the division lemma to 5522 and 645, to get

5522 = 645 x 8 + 362

Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 362 and 645, to get

645 = 362 x 1 + 283

Step 3: We consider the new divisor 362 and the new remainder 283, and apply the division lemma to get

362 = 283 x 1 + 79

We consider the new divisor 283 and the new remainder 79,and apply the division lemma to get

283 = 79 x 3 + 46

We consider the new divisor 79 and the new remainder 46,and apply the division lemma to get

79 = 46 x 1 + 33

We consider the new divisor 46 and the new remainder 33,and apply the division lemma to get

46 = 33 x 1 + 13

We consider the new divisor 33 and the new remainder 13,and apply the division lemma to get

33 = 13 x 2 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 645 and 5522 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(33,13) = HCF(46,33) = HCF(79,46) = HCF(283,79) = HCF(362,283) = HCF(645,362) = HCF(5522,645) .

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Frequently Asked Questions on HCF of 645, 5522 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, 5522?

Answer: HCF of 645, 5522 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 645, 5522 using Euclid's Algorithm?

Answer: For arbitrary numbers 645, 5522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.