Highest Common Factor of 645, 223, 693 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, 223, 693 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 645, 223, 693 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, 223, 693 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, 223, 693 is 1.

HCF(645, 223, 693) = 1

HCF of 645, 223, 693 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, 223, 693 is 1.

Highest Common Factor of 645,223,693 using Euclid's algorithm

Highest Common Factor of 645,223,693 is 1

Step 1: Since 645 > 223, we apply the division lemma to 645 and 223, to get

645 = 223 x 2 + 199

Step 2: Since the reminder 223 ≠ 0, we apply division lemma to 199 and 223, to get

223 = 199 x 1 + 24

Step 3: We consider the new divisor 199 and the new remainder 24, and apply the division lemma to get

199 = 24 x 8 + 7

We consider the new divisor 24 and the new remainder 7,and apply the division lemma to get

24 = 7 x 3 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 645 and 223 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(24,7) = HCF(199,24) = HCF(223,199) = HCF(645,223) .

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

Step 1: Since 693 > 1, we apply the division lemma to 693 and 1, to get

693 = 1 x 693 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 693 is 1

Notice that 1 = HCF(693,1) .

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Frequently Asked Questions on HCF of 645, 223, 693 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, 223, 693?

Answer: HCF of 645, 223, 693 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 645, 223, 693 using Euclid's Algorithm?

Answer: For arbitrary numbers 645, 223, 693 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.