Highest Common Factor of 234, 875, 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 234, 875, 310 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 234, 875, 310 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 234, 875, 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 234, 875, 310 is 1.

HCF(234, 875, 310) = 1

HCF of 234, 875, 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 234, 875, 310 is 1.

Highest Common Factor of 234,875,310 using Euclid's algorithm

Highest Common Factor of 234,875,310 is 1

Step 1: Since 875 > 234, we apply the division lemma to 875 and 234, to get

875 = 234 x 3 + 173

Step 2: Since the reminder 234 ≠ 0, we apply division lemma to 173 and 234, to get

234 = 173 x 1 + 61

Step 3: We consider the new divisor 173 and the new remainder 61, and apply the division lemma to get

173 = 61 x 2 + 51

We consider the new divisor 61 and the new remainder 51,and apply the division lemma to get

61 = 51 x 1 + 10

We consider the new divisor 51 and the new remainder 10,and apply the division lemma to get

51 = 10 x 5 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 234 and 875 is 1

Notice that 1 = HCF(10,1) = HCF(51,10) = HCF(61,51) = HCF(173,61) = HCF(234,173) = HCF(875,234) .

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

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

310 = 1 x 310 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 310 is 1

Notice that 1 = HCF(310,1) .

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Frequently Asked Questions on HCF of 234, 875, 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 234, 875, 310?

Answer: HCF of 234, 875, 310 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 234, 875, 310 using Euclid's Algorithm?

Answer: For arbitrary numbers 234, 875, 310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.