Highest Common Factor of 375, 130, 132 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 375, 130, 132 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 375, 130, 132 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 375, 130, 132 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 375, 130, 132 is 1.

HCF(375, 130, 132) = 1

HCF of 375, 130, 132 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 375, 130, 132 is 1.

Highest Common Factor of 375,130,132 using Euclid's algorithm

Highest Common Factor of 375,130,132 is 1

Step 1: Since 375 > 130, we apply the division lemma to 375 and 130, to get

375 = 130 x 2 + 115

Step 2: Since the reminder 130 ≠ 0, we apply division lemma to 115 and 130, to get

130 = 115 x 1 + 15

Step 3: We consider the new divisor 115 and the new remainder 15, and apply the division lemma to get

115 = 15 x 7 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 375 and 130 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(115,15) = HCF(130,115) = HCF(375,130) .

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

Step 1: Since 132 > 5, we apply the division lemma to 132 and 5, to get

132 = 5 x 26 + 2

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get

5 = 2 x 2 + 1

Step 3: 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 5 and 132 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(132,5) .

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Frequently Asked Questions on HCF of 375, 130, 132 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 375, 130, 132?

Answer: HCF of 375, 130, 132 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 375, 130, 132 using Euclid's Algorithm?

Answer: For arbitrary numbers 375, 130, 132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.