Highest Common Factor of 660, 225, 464, 614 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, 225, 464, 614 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 660, 225, 464, 614 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 660, 225, 464, 614 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, 225, 464, 614 is 1.

HCF(660, 225, 464, 614) = 1

HCF of 660, 225, 464, 614 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 660, 225, 464, 614 is 1.

Highest Common Factor of 660,225,464,614 using Euclid's algorithm

Highest Common Factor of 660,225,464,614 is 1

Step 1: Since 660 > 225, we apply the division lemma to 660 and 225, to get

660 = 225 x 2 + 210

Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 210 and 225, to get

225 = 210 x 1 + 15

Step 3: We consider the new divisor 210 and the new remainder 15, and apply the division lemma to get

210 = 15 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 660 and 225 is 15

Notice that 15 = HCF(210,15) = HCF(225,210) = HCF(660,225) .

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

Step 1: Since 464 > 15, we apply the division lemma to 464 and 15, to get

464 = 15 x 30 + 14

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 14 and 15, to get

15 = 14 x 1 + 1

Step 3: We consider the new divisor 14 and the new remainder 1, and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 464 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(464,15) .

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

Step 1: Since 614 > 1, we apply the division lemma to 614 and 1, to get

614 = 1 x 614 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 614 is 1

Notice that 1 = HCF(614,1) .

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Frequently Asked Questions on HCF of 660, 225, 464, 614 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, 225, 464, 614?

Answer: HCF of 660, 225, 464, 614 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 660, 225, 464, 614 using Euclid's Algorithm?

Answer: For arbitrary numbers 660, 225, 464, 614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.