Highest Common Factor of 2102, 6160 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 2102, 6160 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2102, 6160 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 2102, 6160 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 2102, 6160 is 2.
HCF(2102, 6160) = 2
HCF of 2102, 6160 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2102, 6160 is 2.
Highest Common Factor of 2102,6160 is 2
Step 1: Since 6160 > 2102, we apply the division lemma to 6160 and 2102, to get
6160 = 2102 x 2 + 1956
Step 2: Since the reminder 2102 ≠ 0, we apply division lemma to 1956 and 2102, to get
2102 = 1956 x 1 + 146
Step 3: We consider the new divisor 1956 and the new remainder 146, and apply the division lemma to get
1956 = 146 x 13 + 58
We consider the new divisor 146 and the new remainder 58,and apply the division lemma to get
146 = 58 x 2 + 30
We consider the new divisor 58 and the new remainder 30,and apply the division lemma to get
58 = 30 x 1 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2102 and 6160 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(58,30) = HCF(146,58) = HCF(1956,146) = HCF(2102,1956) = HCF(6160,2102) .
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Frequently Asked Questions on HCF of 2102, 6160 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 2102, 6160?
Answer: HCF of 2102, 6160 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2102, 6160 using Euclid's Algorithm?
Answer: For arbitrary numbers 2102, 6160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.