Highest Common Factor of 1909, 2161 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 1909, 2161 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1909, 2161 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 1909, 2161 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 1909, 2161 is 1.
HCF(1909, 2161) = 1
HCF of 1909, 2161 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1909, 2161 is 1.
Highest Common Factor of 1909,2161 is 1
Step 1: Since 2161 > 1909, we apply the division lemma to 2161 and 1909, to get
2161 = 1909 x 1 + 252
Step 2: Since the reminder 1909 ≠ 0, we apply division lemma to 252 and 1909, to get
1909 = 252 x 7 + 145
Step 3: We consider the new divisor 252 and the new remainder 145, and apply the division lemma to get
252 = 145 x 1 + 107
We consider the new divisor 145 and the new remainder 107,and apply the division lemma to get
145 = 107 x 1 + 38
We consider the new divisor 107 and the new remainder 38,and apply the division lemma to get
107 = 38 x 2 + 31
We consider the new divisor 38 and the new remainder 31,and apply the division lemma to get
38 = 31 x 1 + 7
We consider the new divisor 31 and the new remainder 7,and apply the division lemma to get
31 = 7 x 4 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1909 and 2161 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(31,7) = HCF(38,31) = HCF(107,38) = HCF(145,107) = HCF(252,145) = HCF(1909,252) = HCF(2161,1909) .
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Frequently Asked Questions on HCF of 1909, 2161 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 1909, 2161?
Answer: HCF of 1909, 2161 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1909, 2161 using Euclid's Algorithm?
Answer: For arbitrary numbers 1909, 2161 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.