Highest Common Factor of 513, 908, 223 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, 908, 223 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 513, 908, 223 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, 908, 223 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, 908, 223 is 1.

HCF(513, 908, 223) = 1

HCF of 513, 908, 223 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, 908, 223 is 1.

Highest Common Factor of 513,908,223 using Euclid's algorithm

Highest Common Factor of 513,908,223 is 1

Step 1: Since 908 > 513, we apply the division lemma to 908 and 513, to get

908 = 513 x 1 + 395

Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 395 and 513, to get

513 = 395 x 1 + 118

Step 3: We consider the new divisor 395 and the new remainder 118, and apply the division lemma to get

395 = 118 x 3 + 41

We consider the new divisor 118 and the new remainder 41,and apply the division lemma to get

118 = 41 x 2 + 36

We consider the new divisor 41 and the new remainder 36,and apply the division lemma to get

41 = 36 x 1 + 5

We consider the new divisor 36 and the new remainder 5,and apply the division lemma to get

36 = 5 x 7 + 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 908 is 1

Notice that 1 = HCF(5,1) = HCF(36,5) = HCF(41,36) = HCF(118,41) = HCF(395,118) = HCF(513,395) = HCF(908,513) .

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

Step 1: Since 223 > 1, we apply the division lemma to 223 and 1, to get

223 = 1 x 223 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 223 is 1

Notice that 1 = HCF(223,1) .

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Frequently Asked Questions on HCF of 513, 908, 223 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, 908, 223?

Answer: HCF of 513, 908, 223 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 513, 908, 223 using Euclid's Algorithm?

Answer: For arbitrary numbers 513, 908, 223 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.