Highest Common Factor of 209, 345 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, 345 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 209, 345 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, 345 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, 345 is 1.
HCF(209, 345) = 1
HCF of 209, 345 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, 345 is 1.
Highest Common Factor of 209,345 is 1
Step 1: Since 345 > 209, we apply the division lemma to 345 and 209, to get
345 = 209 x 1 + 136
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 136 and 209, to get
209 = 136 x 1 + 73
Step 3: We consider the new divisor 136 and the new remainder 73, and apply the division lemma to get
136 = 73 x 1 + 63
We consider the new divisor 73 and the new remainder 63,and apply the division lemma to get
73 = 63 x 1 + 10
We consider the new divisor 63 and the new remainder 10,and apply the division lemma to get
63 = 10 x 6 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 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 209 and 345 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(63,10) = HCF(73,63) = HCF(136,73) = HCF(209,136) = HCF(345,209) .
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Frequently Asked Questions on HCF of 209, 345 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, 345?
Answer: HCF of 209, 345 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 209, 345 using Euclid's Algorithm?
Answer: For arbitrary numbers 209, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.