Highest Common Factor of 999, 820, 559 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 999, 820, 559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 999, 820, 559 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 999, 820, 559 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 999, 820, 559 is 1.
HCF(999, 820, 559) = 1
HCF of 999, 820, 559 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 999, 820, 559 is 1.
Highest Common Factor of 999,820,559 is 1
Step 1: Since 999 > 820, we apply the division lemma to 999 and 820, to get
999 = 820 x 1 + 179
Step 2: Since the reminder 820 ≠ 0, we apply division lemma to 179 and 820, to get
820 = 179 x 4 + 104
Step 3: We consider the new divisor 179 and the new remainder 104, and apply the division lemma to get
179 = 104 x 1 + 75
We consider the new divisor 104 and the new remainder 75,and apply the division lemma to get
104 = 75 x 1 + 29
We consider the new divisor 75 and the new remainder 29,and apply the division lemma to get
75 = 29 x 2 + 17
We consider the new divisor 29 and the new remainder 17,and apply the division lemma to get
29 = 17 x 1 + 12
We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get
17 = 12 x 1 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 999 and 820 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(29,17) = HCF(75,29) = HCF(104,75) = HCF(179,104) = HCF(820,179) = HCF(999,820) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 559 > 1, we apply the division lemma to 559 and 1, to get
559 = 1 x 559 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 559 is 1
Notice that 1 = HCF(559,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 999, 820, 559 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 999, 820, 559?
Answer: HCF of 999, 820, 559 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 999, 820, 559 using Euclid's Algorithm?
Answer: For arbitrary numbers 999, 820, 559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
