Highest Common Factor of 209, 161 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 209, 161 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 209, 161 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 209, 161 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 209, 161 is 1.
HCF(209, 161) = 1
HCF of 209, 161 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 209, 161 is 1.
Highest Common Factor of 209,161 is 1
Step 1: Since 209 > 161, we apply the division lemma to 209 and 161, to get
209 = 161 x 1 + 48
Step 2: Since the reminder 161 ≠ 0, we apply division lemma to 48 and 161, to get
161 = 48 x 3 + 17
Step 3: We consider the new divisor 48 and the new remainder 17, and apply the division lemma to get
48 = 17 x 2 + 14
We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get
17 = 14 x 1 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 209 and 161 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(48,17) = HCF(161,48) = HCF(209,161) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 209, 161 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 209, 161?
Answer: HCF of 209, 161 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 209, 161 using Euclid's Algorithm?
Answer: For arbitrary numbers 209, 161 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.