Highest Common Factor of 129, 2010 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 129, 2010 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 129, 2010 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 129, 2010 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 129, 2010 is 3.
HCF(129, 2010) = 3
HCF of 129, 2010 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 129, 2010 is 3.
Highest Common Factor of 129,2010 is 3
Step 1: Since 2010 > 129, we apply the division lemma to 2010 and 129, to get
2010 = 129 x 15 + 75
Step 2: Since the reminder 129 ≠ 0, we apply division lemma to 75 and 129, to get
129 = 75 x 1 + 54
Step 3: We consider the new divisor 75 and the new remainder 54, and apply the division lemma to get
75 = 54 x 1 + 21
We consider the new divisor 54 and the new remainder 21,and apply the division lemma to get
54 = 21 x 2 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 129 and 2010 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(54,21) = HCF(75,54) = HCF(129,75) = HCF(2010,129) .
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Frequently Asked Questions on HCF of 129, 2010 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 129, 2010?
Answer: HCF of 129, 2010 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 129, 2010 using Euclid's Algorithm?
Answer: For arbitrary numbers 129, 2010 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.