Highest Common Factor of 3578, 2203 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 3578, 2203 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3578, 2203 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 3578, 2203 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 3578, 2203 is 1.

HCF(3578, 2203) = 1

HCF of 3578, 2203 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 3578, 2203 is 1.

Highest Common Factor of 3578,2203 using Euclid's algorithm

Highest Common Factor of 3578,2203 is 1

Step 1: Since 3578 > 2203, we apply the division lemma to 3578 and 2203, to get

3578 = 2203 x 1 + 1375

Step 2: Since the reminder 2203 ≠ 0, we apply division lemma to 1375 and 2203, to get

2203 = 1375 x 1 + 828

Step 3: We consider the new divisor 1375 and the new remainder 828, and apply the division lemma to get

1375 = 828 x 1 + 547

We consider the new divisor 828 and the new remainder 547,and apply the division lemma to get

828 = 547 x 1 + 281

We consider the new divisor 547 and the new remainder 281,and apply the division lemma to get

547 = 281 x 1 + 266

We consider the new divisor 281 and the new remainder 266,and apply the division lemma to get

281 = 266 x 1 + 15

We consider the new divisor 266 and the new remainder 15,and apply the division lemma to get

266 = 15 x 17 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 3578 and 2203 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(266,15) = HCF(281,266) = HCF(547,281) = HCF(828,547) = HCF(1375,828) = HCF(2203,1375) = HCF(3578,2203) .

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Frequently Asked Questions on HCF of 3578, 2203 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 3578, 2203?

Answer: HCF of 3578, 2203 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3578, 2203 using Euclid's Algorithm?

Answer: For arbitrary numbers 3578, 2203 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.