Highest Common Factor of 660, 480, 434 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 660, 480, 434 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 660, 480, 434 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 660, 480, 434 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 660, 480, 434 is 2.

HCF(660, 480, 434) = 2

HCF of 660, 480, 434 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 660, 480, 434 is 2.

Highest Common Factor of 660,480,434 using Euclid's algorithm

Highest Common Factor of 660,480,434 is 2

Step 1: Since 660 > 480, we apply the division lemma to 660 and 480, to get

660 = 480 x 1 + 180

Step 2: Since the reminder 480 ≠ 0, we apply division lemma to 180 and 480, to get

480 = 180 x 2 + 120

Step 3: We consider the new divisor 180 and the new remainder 120, and apply the division lemma to get

180 = 120 x 1 + 60

We consider the new divisor 120 and the new remainder 60, and apply the division lemma to get

120 = 60 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 60, the HCF of 660 and 480 is 60

Notice that 60 = HCF(120,60) = HCF(180,120) = HCF(480,180) = HCF(660,480) .

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

Step 1: Since 434 > 60, we apply the division lemma to 434 and 60, to get

434 = 60 x 7 + 14

Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 14 and 60, to get

60 = 14 x 4 + 4

Step 3: We consider the new divisor 14 and the new remainder 4, and apply the division lemma to get

14 = 4 x 3 + 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 60 and 434 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(60,14) = HCF(434,60) .

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Frequently Asked Questions on HCF of 660, 480, 434 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 660, 480, 434?

Answer: HCF of 660, 480, 434 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 660, 480, 434 using Euclid's Algorithm?

Answer: For arbitrary numbers 660, 480, 434 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.