Highest Common Factor of 645, 364, 900 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, 364, 900 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 645, 364, 900 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, 364, 900 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, 364, 900 is 1.

HCF(645, 364, 900) = 1

HCF of 645, 364, 900 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, 364, 900 is 1.

Highest Common Factor of 645,364,900 using Euclid's algorithm

Highest Common Factor of 645,364,900 is 1

Step 1: Since 645 > 364, we apply the division lemma to 645 and 364, to get

645 = 364 x 1 + 281

Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 281 and 364, to get

364 = 281 x 1 + 83

Step 3: We consider the new divisor 281 and the new remainder 83, and apply the division lemma to get

281 = 83 x 3 + 32

We consider the new divisor 83 and the new remainder 32,and apply the division lemma to get

83 = 32 x 2 + 19

We consider the new divisor 32 and the new remainder 19,and apply the division lemma to get

32 = 19 x 1 + 13

We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get

19 = 13 x 1 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 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 364 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(32,19) = HCF(83,32) = HCF(281,83) = HCF(364,281) = HCF(645,364) .

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

Step 1: Since 900 > 1, we apply the division lemma to 900 and 1, to get

900 = 1 x 900 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 900 is 1

Notice that 1 = HCF(900,1) .

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Frequently Asked Questions on HCF of 645, 364, 900 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, 364, 900?

Answer: HCF of 645, 364, 900 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 645, 364, 900 using Euclid's Algorithm?

Answer: For arbitrary numbers 645, 364, 900 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.