Highest Common Factor of 485, 660, 224 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 485, 660, 224 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 485, 660, 224 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 485, 660, 224 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 485, 660, 224 is 1.

HCF(485, 660, 224) = 1

HCF of 485, 660, 224 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 485, 660, 224 is 1.

Highest Common Factor of 485,660,224 using Euclid's algorithm

Highest Common Factor of 485,660,224 is 1

Step 1: Since 660 > 485, we apply the division lemma to 660 and 485, to get

660 = 485 x 1 + 175

Step 2: Since the reminder 485 ≠ 0, we apply division lemma to 175 and 485, to get

485 = 175 x 2 + 135

Step 3: We consider the new divisor 175 and the new remainder 135, and apply the division lemma to get

175 = 135 x 1 + 40

We consider the new divisor 135 and the new remainder 40,and apply the division lemma to get

135 = 40 x 3 + 15

We consider the new divisor 40 and the new remainder 15,and apply the division lemma to get

40 = 15 x 2 + 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 485 and 660 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(135,40) = HCF(175,135) = HCF(485,175) = HCF(660,485) .

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

Step 1: Since 224 > 5, we apply the division lemma to 224 and 5, to get

224 = 5 x 44 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 224 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(224,5) .

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Frequently Asked Questions on HCF of 485, 660, 224 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 485, 660, 224?

Answer: HCF of 485, 660, 224 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 485, 660, 224 using Euclid's Algorithm?

Answer: For arbitrary numbers 485, 660, 224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.