Highest Common Factor of 2042, 2184 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 2042, 2184 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2042, 2184 is 2 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 2042, 2184 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 2042, 2184 is 2.
HCF(2042, 2184) = 2
HCF of 2042, 2184 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2042, 2184 is 2.
Highest Common Factor of 2042,2184 is 2
Step 1: Since 2184 > 2042, we apply the division lemma to 2184 and 2042, to get
2184 = 2042 x 1 + 142
Step 2: Since the reminder 2042 ≠ 0, we apply division lemma to 142 and 2042, to get
2042 = 142 x 14 + 54
Step 3: We consider the new divisor 142 and the new remainder 54, and apply the division lemma to get
142 = 54 x 2 + 34
We consider the new divisor 54 and the new remainder 34,and apply the division lemma to get
54 = 34 x 1 + 20
We consider the new divisor 34 and the new remainder 20,and apply the division lemma to get
34 = 20 x 1 + 14
We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 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 2042 and 2184 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(34,20) = HCF(54,34) = HCF(142,54) = HCF(2042,142) = HCF(2184,2042) .
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Frequently Asked Questions on HCF of 2042, 2184 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 2042, 2184?
Answer: HCF of 2042, 2184 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2042, 2184 using Euclid's Algorithm?
Answer: For arbitrary numbers 2042, 2184 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.