Highest Common Factor of 232, 642, 310 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 232, 642, 310 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 232, 642, 310 is 2 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 232, 642, 310 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 232, 642, 310 is 2.

HCF(232, 642, 310) = 2

HCF of 232, 642, 310 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 232, 642, 310 is 2.

Highest Common Factor of 232,642,310 using Euclid's algorithm

Highest Common Factor of 232,642,310 is 2

Step 1: Since 642 > 232, we apply the division lemma to 642 and 232, to get

642 = 232 x 2 + 178

Step 2: Since the reminder 232 ≠ 0, we apply division lemma to 178 and 232, to get

232 = 178 x 1 + 54

Step 3: We consider the new divisor 178 and the new remainder 54, and apply the division lemma to get

178 = 54 x 3 + 16

We consider the new divisor 54 and the new remainder 16,and apply the division lemma to get

54 = 16 x 3 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 232 and 642 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(54,16) = HCF(178,54) = HCF(232,178) = HCF(642,232) .

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

Step 1: Since 310 > 2, we apply the division lemma to 310 and 2, to get

310 = 2 x 155 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 310 is 2

Notice that 2 = HCF(310,2) .

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Frequently Asked Questions on HCF of 232, 642, 310 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 232, 642, 310?

Answer: HCF of 232, 642, 310 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 232, 642, 310 using Euclid's Algorithm?

Answer: For arbitrary numbers 232, 642, 310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.