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, 4155 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 305, 4155 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, 4155 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, 4155 is 5.
HCF(305, 4155) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 305, 4155 is 5.
Step 1: Since 4155 > 305, we apply the division lemma to 4155 and 305, to get
4155 = 305 x 13 + 190
Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 190 and 305, to get
305 = 190 x 1 + 115
Step 3: We consider the new divisor 190 and the new remainder 115, and apply the division lemma to get
190 = 115 x 1 + 75
We consider the new divisor 115 and the new remainder 75,and apply the division lemma to get
115 = 75 x 1 + 40
We consider the new divisor 75 and the new remainder 40,and apply the division lemma to get
75 = 40 x 1 + 35
We consider the new divisor 40 and the new remainder 35,and apply the division lemma to get
40 = 35 x 1 + 5
We consider the new divisor 35 and the new remainder 5,and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 305 and 4155 is 5
Notice that 5 = HCF(35,5) = HCF(40,35) = HCF(75,40) = HCF(115,75) = HCF(190,115) = HCF(305,190) = HCF(4155,305) .
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, 4155?
Answer: HCF of 305, 4155 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 305, 4155 using Euclid's Algorithm?
Answer: For arbitrary numbers 305, 4155 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.