Highest Common Factor of 132, 442, 413, 218 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 132, 442, 413, 218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 132, 442, 413, 218 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 132, 442, 413, 218 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 132, 442, 413, 218 is 1.

HCF(132, 442, 413, 218) = 1

HCF of 132, 442, 413, 218 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 132, 442, 413, 218 is 1.

Highest Common Factor of 132,442,413,218 using Euclid's algorithm

Highest Common Factor of 132,442,413,218 is 1

Step 1: Since 442 > 132, we apply the division lemma to 442 and 132, to get

442 = 132 x 3 + 46

Step 2: Since the reminder 132 ≠ 0, we apply division lemma to 46 and 132, to get

132 = 46 x 2 + 40

Step 3: We consider the new divisor 46 and the new remainder 40, and apply the division lemma to get

46 = 40 x 1 + 6

We consider the new divisor 40 and the new remainder 6,and apply the division lemma to get

40 = 6 x 6 + 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 132 and 442 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(40,6) = HCF(46,40) = HCF(132,46) = HCF(442,132) .

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

Step 1: Since 413 > 2, we apply the division lemma to 413 and 2, to get

413 = 2 x 206 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 413 is 1

Notice that 1 = HCF(2,1) = HCF(413,2) .

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

Step 1: Since 218 > 1, we apply the division lemma to 218 and 1, to get

218 = 1 x 218 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 218 is 1

Notice that 1 = HCF(218,1) .

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Frequently Asked Questions on HCF of 132, 442, 413, 218 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 132, 442, 413, 218?

Answer: HCF of 132, 442, 413, 218 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 132, 442, 413, 218 using Euclid's Algorithm?

Answer: For arbitrary numbers 132, 442, 413, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.