Highest Common Factor of 505, 305 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 505, 305 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 505, 305 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 505, 305 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 505, 305 is 5.
HCF(505, 305) = 5
HCF of 505, 305 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 505, 305 is 5.
Highest Common Factor of 505,305 is 5
Step 1: Since 505 > 305, we apply the division lemma to 505 and 305, to get
505 = 305 x 1 + 200
Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 200 and 305, to get
305 = 200 x 1 + 105
Step 3: We consider the new divisor 200 and the new remainder 105, and apply the division lemma to get
200 = 105 x 1 + 95
We consider the new divisor 105 and the new remainder 95,and apply the division lemma to get
105 = 95 x 1 + 10
We consider the new divisor 95 and the new remainder 10,and apply the division lemma to get
95 = 10 x 9 + 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 505 and 305 is 5
Notice that 5 = HCF(10,5) = HCF(95,10) = HCF(105,95) = HCF(200,105) = HCF(305,200) = HCF(505,305) .
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Frequently Asked Questions on HCF of 505, 305 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 505, 305?
Answer: HCF of 505, 305 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 505, 305 using Euclid's Algorithm?
Answer: For arbitrary numbers 505, 305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.