Highest Common Factor of 630, 882, 173 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, 882, 173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 630, 882, 173 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 630, 882, 173 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, 882, 173 is 1.

HCF(630, 882, 173) = 1

HCF of 630, 882, 173 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, 882, 173 is 1.

Highest Common Factor of 630,882,173 using Euclid's algorithm

Highest Common Factor of 630,882,173 is 1

Step 1: Since 882 > 630, we apply the division lemma to 882 and 630, to get

882 = 630 x 1 + 252

Step 2: Since the reminder 630 ≠ 0, we apply division lemma to 252 and 630, to get

630 = 252 x 2 + 126

Step 3: We consider the new divisor 252 and the new remainder 126, and apply the division lemma to get

252 = 126 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 126, the HCF of 630 and 882 is 126

Notice that 126 = HCF(252,126) = HCF(630,252) = HCF(882,630) .

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

Step 1: Since 173 > 126, we apply the division lemma to 173 and 126, to get

173 = 126 x 1 + 47

Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 47 and 126, to get

126 = 47 x 2 + 32

Step 3: We consider the new divisor 47 and the new remainder 32, and apply the division lemma to get

47 = 32 x 1 + 15

We consider the new divisor 32 and the new remainder 15,and apply the division lemma to get

32 = 15 x 2 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 126 and 173 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(32,15) = HCF(47,32) = HCF(126,47) = HCF(173,126) .

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Frequently Asked Questions on HCF of 630, 882, 173 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, 882, 173?

Answer: HCF of 630, 882, 173 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 630, 882, 173 using Euclid's Algorithm?

Answer: For arbitrary numbers 630, 882, 173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.