Highest Common Factor of 480, 645, 118 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 480, 645, 118 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 480, 645, 118 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 480, 645, 118 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 480, 645, 118 is 1.

HCF(480, 645, 118) = 1

HCF of 480, 645, 118 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 480, 645, 118 is 1.

Highest Common Factor of 480,645,118 using Euclid's algorithm

Highest Common Factor of 480,645,118 is 1

Step 1: Since 645 > 480, we apply the division lemma to 645 and 480, to get

645 = 480 x 1 + 165

Step 2: Since the reminder 480 ≠ 0, we apply division lemma to 165 and 480, to get

480 = 165 x 2 + 150

Step 3: We consider the new divisor 165 and the new remainder 150, and apply the division lemma to get

165 = 150 x 1 + 15

We consider the new divisor 150 and the new remainder 15, and apply the division lemma to get

150 = 15 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 480 and 645 is 15

Notice that 15 = HCF(150,15) = HCF(165,150) = HCF(480,165) = HCF(645,480) .

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

Step 1: Since 118 > 15, we apply the division lemma to 118 and 15, to get

118 = 15 x 7 + 13

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 13 and 15, to get

15 = 13 x 1 + 2

Step 3: We consider the new divisor 13 and the new remainder 2, and apply the division lemma to get

13 = 2 x 6 + 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 15 and 118 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(118,15) .

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Frequently Asked Questions on HCF of 480, 645, 118 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 480, 645, 118?

Answer: HCF of 480, 645, 118 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 480, 645, 118 using Euclid's Algorithm?

Answer: For arbitrary numbers 480, 645, 118 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.