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 195, 260, 145 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 195, 260, 145 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 195, 260, 145 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 195, 260, 145 is 5.
HCF(195, 260, 145) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 195, 260, 145 is 5.
Step 1: Since 260 > 195, we apply the division lemma to 260 and 195, to get
260 = 195 x 1 + 65
Step 2: Since the reminder 195 ≠ 0, we apply division lemma to 65 and 195, to get
195 = 65 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 65, the HCF of 195 and 260 is 65
Notice that 65 = HCF(195,65) = HCF(260,195) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 145 > 65, we apply the division lemma to 145 and 65, to get
145 = 65 x 2 + 15
Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 15 and 65, to get
65 = 15 x 4 + 5
Step 3: We consider the new divisor 15 and the new remainder 5, and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 65 and 145 is 5
Notice that 5 = HCF(15,5) = HCF(65,15) = HCF(145,65) .
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 195, 260, 145?
Answer: HCF of 195, 260, 145 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 195, 260, 145 using Euclid's Algorithm?
Answer: For arbitrary numbers 195, 260, 145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.