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 115, 7450, 2186 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 115, 7450, 2186 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 115, 7450, 2186 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 115, 7450, 2186 is 1.
HCF(115, 7450, 2186) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 115, 7450, 2186 is 1.
Step 1: Since 7450 > 115, we apply the division lemma to 7450 and 115, to get
7450 = 115 x 64 + 90
Step 2: Since the reminder 115 ≠ 0, we apply division lemma to 90 and 115, to get
115 = 90 x 1 + 25
Step 3: We consider the new divisor 90 and the new remainder 25, and apply the division lemma to get
90 = 25 x 3 + 15
We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get
25 = 15 x 1 + 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 115 and 7450 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(90,25) = HCF(115,90) = HCF(7450,115) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2186 > 5, we apply the division lemma to 2186 and 5, to get
2186 = 5 x 437 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 2186 is 1
Notice that 1 = HCF(5,1) = HCF(2186,5) .
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 115, 7450, 2186?
Answer: HCF of 115, 7450, 2186 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 115, 7450, 2186 using Euclid's Algorithm?
Answer: For arbitrary numbers 115, 7450, 2186 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.