Highest Common Factor of 180, 600, 519 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 180, 600, 519 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 180, 600, 519 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 180, 600, 519 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 180, 600, 519 is 3.
HCF(180, 600, 519) = 3
HCF of 180, 600, 519 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 180, 600, 519 is 3.
Highest Common Factor of 180,600,519 is 3
Step 1: Since 600 > 180, we apply the division lemma to 600 and 180, to get
600 = 180 x 3 + 60
Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 60 and 180, to get
180 = 60 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 60, the HCF of 180 and 600 is 60
Notice that 60 = HCF(180,60) = HCF(600,180) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 519 > 60, we apply the division lemma to 519 and 60, to get
519 = 60 x 8 + 39
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 39 and 60, to get
60 = 39 x 1 + 21
Step 3: We consider the new divisor 39 and the new remainder 21, and apply the division lemma to get
39 = 21 x 1 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 60 and 519 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(39,21) = HCF(60,39) = HCF(519,60) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 180, 600, 519 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 180, 600, 519?
Answer: HCF of 180, 600, 519 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 180, 600, 519 using Euclid's Algorithm?
Answer: For arbitrary numbers 180, 600, 519 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.