Highest Common Factor of 125, 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 125, 205 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 125, 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 125, 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 125, 205 is 5.
HCF(125, 205) = 5
HCF of 125, 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 125, 205 is 5.
Highest Common Factor of 125,205 is 5
Step 1: Since 205 > 125, we apply the division lemma to 205 and 125, to get
205 = 125 x 1 + 80
Step 2: Since the reminder 125 ≠ 0, we apply division lemma to 80 and 125, to get
125 = 80 x 1 + 45
Step 3: We consider the new divisor 80 and the new remainder 45, and apply the division lemma to get
80 = 45 x 1 + 35
We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get
45 = 35 x 1 + 10
We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get
35 = 10 x 3 + 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 125 and 205 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(80,45) = HCF(125,80) = HCF(205,125) .
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Frequently Asked Questions on HCF of 125, 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 125, 205?
Answer: HCF of 125, 205 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 125, 205 using Euclid's Algorithm?
Answer: For arbitrary numbers 125, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.