Highest Common Factor of 599, 822, 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 599, 822, 513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 599, 822, 513 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 599, 822, 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 599, 822, 513 is 1.

HCF(599, 822, 513) = 1

HCF of 599, 822, 513 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 599, 822, 513 is 1.

Highest Common Factor of 599,822,513 using Euclid's algorithm

Highest Common Factor of 599,822,513 is 1

Step 1: Since 822 > 599, we apply the division lemma to 822 and 599, to get

822 = 599 x 1 + 223

Step 2: Since the reminder 599 ≠ 0, we apply division lemma to 223 and 599, to get

599 = 223 x 2 + 153

Step 3: We consider the new divisor 223 and the new remainder 153, and apply the division lemma to get

223 = 153 x 1 + 70

We consider the new divisor 153 and the new remainder 70,and apply the division lemma to get

153 = 70 x 2 + 13

We consider the new divisor 70 and the new remainder 13,and apply the division lemma to get

70 = 13 x 5 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 599 and 822 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(70,13) = HCF(153,70) = HCF(223,153) = HCF(599,223) = HCF(822,599) .

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

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

513 = 1 x 513 + 0

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

Notice that 1 = HCF(513,1) .

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Frequently Asked Questions on HCF of 599, 822, 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 599, 822, 513?

Answer: HCF of 599, 822, 513 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 599, 822, 513 using Euclid's Algorithm?

Answer: For arbitrary numbers 599, 822, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.