Highest Common Factor of 203, 332, 102 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 203, 332, 102 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 203, 332, 102 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 203, 332, 102 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 203, 332, 102 is 1.

HCF(203, 332, 102) = 1

HCF of 203, 332, 102 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 203, 332, 102 is 1.

Highest Common Factor of 203,332,102 using Euclid's algorithm

Highest Common Factor of 203,332,102 is 1

Step 1: Since 332 > 203, we apply the division lemma to 332 and 203, to get

332 = 203 x 1 + 129

Step 2: Since the reminder 203 ≠ 0, we apply division lemma to 129 and 203, to get

203 = 129 x 1 + 74

Step 3: We consider the new divisor 129 and the new remainder 74, and apply the division lemma to get

129 = 74 x 1 + 55

We consider the new divisor 74 and the new remainder 55,and apply the division lemma to get

74 = 55 x 1 + 19

We consider the new divisor 55 and the new remainder 19,and apply the division lemma to get

55 = 19 x 2 + 17

We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get

19 = 17 x 1 + 2

We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get

17 = 2 x 8 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 203 and 332 is 1

Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(55,19) = HCF(74,55) = HCF(129,74) = HCF(203,129) = HCF(332,203) .

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

Step 1: Since 102 > 1, we apply the division lemma to 102 and 1, to get

102 = 1 x 102 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 102 is 1

Notice that 1 = HCF(102,1) .

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Frequently Asked Questions on HCF of 203, 332, 102 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 203, 332, 102?

Answer: HCF of 203, 332, 102 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 203, 332, 102 using Euclid's Algorithm?

Answer: For arbitrary numbers 203, 332, 102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.