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 235, 60129 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 235, 60129 is 1 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 235, 60129 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 235, 60129 is 1.
HCF(235, 60129) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 235, 60129 is 1.
Step 1: Since 60129 > 235, we apply the division lemma to 60129 and 235, to get
60129 = 235 x 255 + 204
Step 2: Since the reminder 235 ≠ 0, we apply division lemma to 204 and 235, to get
235 = 204 x 1 + 31
Step 3: We consider the new divisor 204 and the new remainder 31, and apply the division lemma to get
204 = 31 x 6 + 18
We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get
31 = 18 x 1 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 235 and 60129 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(204,31) = HCF(235,204) = HCF(60129,235) .
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 235, 60129?
Answer: HCF of 235, 60129 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 235, 60129 using Euclid's Algorithm?
Answer: For arbitrary numbers 235, 60129 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.