Highest Common Factor of 111, 513 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 111, 513 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 111, 513 is 3 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 111, 513 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 111, 513 is 3.

HCF(111, 513) = 3

HCF of 111, 513 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 111, 513 is 3.

Highest Common Factor of 111,513 using Euclid's algorithm

Highest Common Factor of 111,513 is 3

Step 1: Since 513 > 111, we apply the division lemma to 513 and 111, to get

513 = 111 x 4 + 69

Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 69 and 111, to get

111 = 69 x 1 + 42

Step 3: We consider the new divisor 69 and the new remainder 42, and apply the division lemma to get

69 = 42 x 1 + 27

We consider the new divisor 42 and the new remainder 27,and apply the division lemma to get

42 = 27 x 1 + 15

We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get

27 = 15 x 1 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 111 and 513 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(42,27) = HCF(69,42) = HCF(111,69) = HCF(513,111) .

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Frequently Asked Questions on HCF of 111, 513 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 111, 513?

Answer: HCF of 111, 513 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 111, 513 using Euclid's Algorithm?

Answer: For arbitrary numbers 111, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.