Highest Common Factor of 450, 632, 30 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 450, 632, 30 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 450, 632, 30 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 450, 632, 30 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 450, 632, 30 is 2.

HCF(450, 632, 30) = 2

HCF of 450, 632, 30 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 450, 632, 30 is 2.

Highest Common Factor of 450,632,30 using Euclid's algorithm

Highest Common Factor of 450,632,30 is 2

Step 1: Since 632 > 450, we apply the division lemma to 632 and 450, to get

632 = 450 x 1 + 182

Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 182 and 450, to get

450 = 182 x 2 + 86

Step 3: We consider the new divisor 182 and the new remainder 86, and apply the division lemma to get

182 = 86 x 2 + 10

We consider the new divisor 86 and the new remainder 10,and apply the division lemma to get

86 = 10 x 8 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 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 450 and 632 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(86,10) = HCF(182,86) = HCF(450,182) = HCF(632,450) .

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

Step 1: Since 30 > 2, we apply the division lemma to 30 and 2, to get

30 = 2 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 30 is 2

Notice that 2 = HCF(30,2) .

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Frequently Asked Questions on HCF of 450, 632, 30 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 450, 632, 30?

Answer: HCF of 450, 632, 30 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 450, 632, 30 using Euclid's Algorithm?

Answer: For arbitrary numbers 450, 632, 30 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.