Highest Common Factor of 305, 485 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 305, 485 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 305, 485 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 305, 485 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 305, 485 is 5.
HCF(305, 485) = 5
HCF of 305, 485 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 305, 485 is 5.
Highest Common Factor of 305,485 is 5
Step 1: Since 485 > 305, we apply the division lemma to 485 and 305, to get
485 = 305 x 1 + 180
Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 180 and 305, to get
305 = 180 x 1 + 125
Step 3: We consider the new divisor 180 and the new remainder 125, and apply the division lemma to get
180 = 125 x 1 + 55
We consider the new divisor 125 and the new remainder 55,and apply the division lemma to get
125 = 55 x 2 + 15
We consider the new divisor 55 and the new remainder 15,and apply the division lemma to get
55 = 15 x 3 + 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 305 and 485 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(55,15) = HCF(125,55) = HCF(180,125) = HCF(305,180) = HCF(485,305) .
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Frequently Asked Questions on HCF of 305, 485 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 305, 485?
Answer: HCF of 305, 485 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 305, 485 using Euclid's Algorithm?
Answer: For arbitrary numbers 305, 485 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.