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, 500 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 305, 500 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, 500 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, 500 is 5.
HCF(305, 500) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 305, 500 is 5.
Step 1: Since 500 > 305, we apply the division lemma to 500 and 305, to get
500 = 305 x 1 + 195
Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 195 and 305, to get
305 = 195 x 1 + 110
Step 3: We consider the new divisor 195 and the new remainder 110, and apply the division lemma to get
195 = 110 x 1 + 85
We consider the new divisor 110 and the new remainder 85,and apply the division lemma to get
110 = 85 x 1 + 25
We consider the new divisor 85 and the new remainder 25,and apply the division lemma to get
85 = 25 x 3 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 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 500 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(85,25) = HCF(110,85) = HCF(195,110) = HCF(305,195) = HCF(500,305) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 500?
Answer: HCF of 305, 500 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 305, 500 using Euclid's Algorithm?
Answer: For arbitrary numbers 305, 500 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.