Highest Common Factor of 513, 320, 183 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 513, 320, 183 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 513, 320, 183 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 513, 320, 183 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 513, 320, 183 is 1.

HCF(513, 320, 183) = 1

HCF of 513, 320, 183 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 513, 320, 183 is 1.

Highest Common Factor of 513,320,183 using Euclid's algorithm

Highest Common Factor of 513,320,183 is 1

Step 1: Since 513 > 320, we apply the division lemma to 513 and 320, to get

513 = 320 x 1 + 193

Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 193 and 320, to get

320 = 193 x 1 + 127

Step 3: We consider the new divisor 193 and the new remainder 127, and apply the division lemma to get

193 = 127 x 1 + 66

We consider the new divisor 127 and the new remainder 66,and apply the division lemma to get

127 = 66 x 1 + 61

We consider the new divisor 66 and the new remainder 61,and apply the division lemma to get

66 = 61 x 1 + 5

We consider the new divisor 61 and the new remainder 5,and apply the division lemma to get

61 = 5 x 12 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 513 and 320 is 1

Notice that 1 = HCF(5,1) = HCF(61,5) = HCF(66,61) = HCF(127,66) = HCF(193,127) = HCF(320,193) = HCF(513,320) .

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

Step 1: Since 183 > 1, we apply the division lemma to 183 and 1, to get

183 = 1 x 183 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 183 is 1

Notice that 1 = HCF(183,1) .

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Frequently Asked Questions on HCF of 513, 320, 183 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 513, 320, 183?

Answer: HCF of 513, 320, 183 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 513, 320, 183 using Euclid's Algorithm?

Answer: For arbitrary numbers 513, 320, 183 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.