Highest Common Factor of 412, 578, 999 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 412, 578, 999 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 578, 999 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 412, 578, 999 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 412, 578, 999 is 1.
HCF(412, 578, 999) = 1
HCF of 412, 578, 999 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 578, 999 is 1.
Highest Common Factor of 412,578,999 is 1
Step 1: Since 578 > 412, we apply the division lemma to 578 and 412, to get
578 = 412 x 1 + 166
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 166 and 412, to get
412 = 166 x 2 + 80
Step 3: We consider the new divisor 166 and the new remainder 80, and apply the division lemma to get
166 = 80 x 2 + 6
We consider the new divisor 80 and the new remainder 6,and apply the division lemma to get
80 = 6 x 13 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 412 and 578 is 2
Notice that 2 = HCF(6,2) = HCF(80,6) = HCF(166,80) = HCF(412,166) = HCF(578,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 999 > 2, we apply the division lemma to 999 and 2, to get
999 = 2 x 499 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 999 is 1
Notice that 1 = HCF(2,1) = HCF(999,2) .
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Frequently Asked Questions on HCF of 412, 578, 999 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 412, 578, 999?
Answer: HCF of 412, 578, 999 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 578, 999 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 578, 999 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
