Highest Common Factor of 320, 205 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 320, 205 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 320, 205 is 5 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 320, 205 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 320, 205 is 5.
HCF(320, 205) = 5
HCF of 320, 205 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 320, 205 is 5.
Highest Common Factor of 320,205 is 5
Step 1: Since 320 > 205, we apply the division lemma to 320 and 205, to get
320 = 205 x 1 + 115
Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 115 and 205, to get
205 = 115 x 1 + 90
Step 3: We consider the new divisor 115 and the new remainder 90, and apply the division lemma to get
115 = 90 x 1 + 25
We consider the new divisor 90 and the new remainder 25,and apply the division lemma to get
90 = 25 x 3 + 15
We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get
25 = 15 x 1 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 320 and 205 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(90,25) = HCF(115,90) = HCF(205,115) = HCF(320,205) .
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Frequently Asked Questions on HCF of 320, 205 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 320, 205?
Answer: HCF of 320, 205 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 320, 205 using Euclid's Algorithm?
Answer: For arbitrary numbers 320, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.