Highest Common Factor of 644, 990, 213 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 644, 990, 213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 644, 990, 213 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 644, 990, 213 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 644, 990, 213 is 1.

HCF(644, 990, 213) = 1

HCF of 644, 990, 213 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 644, 990, 213 is 1.

Highest Common Factor of 644,990,213 using Euclid's algorithm

Highest Common Factor of 644,990,213 is 1

Step 1: Since 990 > 644, we apply the division lemma to 990 and 644, to get

990 = 644 x 1 + 346

Step 2: Since the reminder 644 ≠ 0, we apply division lemma to 346 and 644, to get

644 = 346 x 1 + 298

Step 3: We consider the new divisor 346 and the new remainder 298, and apply the division lemma to get

346 = 298 x 1 + 48

We consider the new divisor 298 and the new remainder 48,and apply the division lemma to get

298 = 48 x 6 + 10

We consider the new divisor 48 and the new remainder 10,and apply the division lemma to get

48 = 10 x 4 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 644 and 990 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(48,10) = HCF(298,48) = HCF(346,298) = HCF(644,346) = HCF(990,644) .

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

Step 1: Since 213 > 2, we apply the division lemma to 213 and 2, to get

213 = 2 x 106 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 213 is 1

Notice that 1 = HCF(2,1) = HCF(213,2) .

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Frequently Asked Questions on HCF of 644, 990, 213 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 644, 990, 213?

Answer: HCF of 644, 990, 213 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 644, 990, 213 using Euclid's Algorithm?

Answer: For arbitrary numbers 644, 990, 213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.