Highest Common Factor of 415, 661, 480 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 415, 661, 480 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 415, 661, 480 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 415, 661, 480 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 415, 661, 480 is 1.

HCF(415, 661, 480) = 1

HCF of 415, 661, 480 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 415, 661, 480 is 1.

Highest Common Factor of 415,661,480 using Euclid's algorithm

Highest Common Factor of 415,661,480 is 1

Step 1: Since 661 > 415, we apply the division lemma to 661 and 415, to get

661 = 415 x 1 + 246

Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 246 and 415, to get

415 = 246 x 1 + 169

Step 3: We consider the new divisor 246 and the new remainder 169, and apply the division lemma to get

246 = 169 x 1 + 77

We consider the new divisor 169 and the new remainder 77,and apply the division lemma to get

169 = 77 x 2 + 15

We consider the new divisor 77 and the new remainder 15,and apply the division lemma to get

77 = 15 x 5 + 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 415 and 661 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(77,15) = HCF(169,77) = HCF(246,169) = HCF(415,246) = HCF(661,415) .

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

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

480 = 1 x 480 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 480 is 1

Notice that 1 = HCF(480,1) .

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Frequently Asked Questions on HCF of 415, 661, 480 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 415, 661, 480?

Answer: HCF of 415, 661, 480 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 415, 661, 480 using Euclid's Algorithm?

Answer: For arbitrary numbers 415, 661, 480 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.