Highest Common Factor of 370, 203 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 370, 203 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 370, 203 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 370, 203 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 370, 203 is 1.

HCF(370, 203) = 1

HCF of 370, 203 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 370, 203 is 1.

Highest Common Factor of 370,203 using Euclid's algorithm

Highest Common Factor of 370,203 is 1

Step 1: Since 370 > 203, we apply the division lemma to 370 and 203, to get

370 = 203 x 1 + 167

Step 2: Since the reminder 203 ≠ 0, we apply division lemma to 167 and 203, to get

203 = 167 x 1 + 36

Step 3: We consider the new divisor 167 and the new remainder 36, and apply the division lemma to get

167 = 36 x 4 + 23

We consider the new divisor 36 and the new remainder 23,and apply the division lemma to get

36 = 23 x 1 + 13

We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get

23 = 13 x 1 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 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 370 and 203 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(36,23) = HCF(167,36) = HCF(203,167) = HCF(370,203) .

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Frequently Asked Questions on HCF of 370, 203 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 370, 203?

Answer: HCF of 370, 203 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 370, 203 using Euclid's Algorithm?

Answer: For arbitrary numbers 370, 203 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.