Highest Common Factor of 355, 520, 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 355, 520, 224 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 355, 520, 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 355, 520, 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 355, 520, 224 is 1.

HCF(355, 520, 224) = 1

HCF of 355, 520, 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 355, 520, 224 is 1.

Highest Common Factor of 355,520,224 using Euclid's algorithm

Highest Common Factor of 355,520,224 is 1

Step 1: Since 520 > 355, we apply the division lemma to 520 and 355, to get

520 = 355 x 1 + 165

Step 2: Since the reminder 355 ≠ 0, we apply division lemma to 165 and 355, to get

355 = 165 x 2 + 25

Step 3: We consider the new divisor 165 and the new remainder 25, and apply the division lemma to get

165 = 25 x 6 + 15

We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get

25 = 15 x 1 + 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 355 and 520 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(165,25) = HCF(355,165) = HCF(520,355) .

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 355, 520, 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 355, 520, 224?

Answer: HCF of 355, 520, 224 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 355, 520, 224 using Euclid's Algorithm?

Answer: For arbitrary numbers 355, 520, 224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.