Highest Common Factor of 630, 856, 232 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 630, 856, 232 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 630, 856, 232 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 630, 856, 232 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 630, 856, 232 is 2.

HCF(630, 856, 232) = 2

HCF of 630, 856, 232 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 630, 856, 232 is 2.

Highest Common Factor of 630,856,232 using Euclid's algorithm

Highest Common Factor of 630,856,232 is 2

Step 1: Since 856 > 630, we apply the division lemma to 856 and 630, to get

856 = 630 x 1 + 226

Step 2: Since the reminder 630 ≠ 0, we apply division lemma to 226 and 630, to get

630 = 226 x 2 + 178

Step 3: We consider the new divisor 226 and the new remainder 178, and apply the division lemma to get

226 = 178 x 1 + 48

We consider the new divisor 178 and the new remainder 48,and apply the division lemma to get

178 = 48 x 3 + 34

We consider the new divisor 48 and the new remainder 34,and apply the division lemma to get

48 = 34 x 1 + 14

We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get

34 = 14 x 2 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 630 and 856 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(48,34) = HCF(178,48) = HCF(226,178) = HCF(630,226) = HCF(856,630) .

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

Step 1: Since 232 > 2, we apply the division lemma to 232 and 2, to get

232 = 2 x 116 + 0

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

Notice that 2 = HCF(232,2) .

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Frequently Asked Questions on HCF of 630, 856, 232 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 630, 856, 232?

Answer: HCF of 630, 856, 232 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 630, 856, 232 using Euclid's Algorithm?

Answer: For arbitrary numbers 630, 856, 232 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.