Highest Common Factor of 2035, 1412 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 2035, 1412 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2035, 1412 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 2035, 1412 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 2035, 1412 is 1.
HCF(2035, 1412) = 1
HCF of 2035, 1412 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2035, 1412 is 1.
Highest Common Factor of 2035,1412 is 1
Step 1: Since 2035 > 1412, we apply the division lemma to 2035 and 1412, to get
2035 = 1412 x 1 + 623
Step 2: Since the reminder 1412 ≠ 0, we apply division lemma to 623 and 1412, to get
1412 = 623 x 2 + 166
Step 3: We consider the new divisor 623 and the new remainder 166, and apply the division lemma to get
623 = 166 x 3 + 125
We consider the new divisor 166 and the new remainder 125,and apply the division lemma to get
166 = 125 x 1 + 41
We consider the new divisor 125 and the new remainder 41,and apply the division lemma to get
125 = 41 x 3 + 2
We consider the new divisor 41 and the new remainder 2,and apply the division lemma to get
41 = 2 x 20 + 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 2035 and 1412 is 1
Notice that 1 = HCF(2,1) = HCF(41,2) = HCF(125,41) = HCF(166,125) = HCF(623,166) = HCF(1412,623) = HCF(2035,1412) .
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Frequently Asked Questions on HCF of 2035, 1412 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 2035, 1412?
Answer: HCF of 2035, 1412 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2035, 1412 using Euclid's Algorithm?
Answer: For arbitrary numbers 2035, 1412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.