Highest Common Factor of 170, 405, 145 using Euclid's algorithm
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 170, 405, 145 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 170, 405, 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 170, 405, 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 170, 405, 145 is 5.
HCF(170, 405, 145) = 5
HCF of 170, 405, 145 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 170, 405, 145 is 5.
Highest Common Factor of 170,405,145 is 5
Step 1: Since 405 > 170, we apply the division lemma to 405 and 170, to get
405 = 170 x 2 + 65
Step 2: Since the reminder 170 ≠ 0, we apply division lemma to 65 and 170, to get
170 = 65 x 2 + 40
Step 3: We consider the new divisor 65 and the new remainder 40, and apply the division lemma to get
65 = 40 x 1 + 25
We consider the new divisor 40 and the new remainder 25,and apply the division lemma to get
40 = 25 x 1 + 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 170 and 405 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(40,25) = HCF(65,40) = HCF(170,65) = HCF(405,170) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 145 > 5, we apply the division lemma to 145 and 5, to get
145 = 5 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 145 is 5
Notice that 5 = HCF(145,5) .
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Frequently Asked Questions on HCF of 170, 405, 145 using Euclid's Algorithm
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 170, 405, 145?
Answer: HCF of 170, 405, 145 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 170, 405, 145 using Euclid's Algorithm?
Answer: For arbitrary numbers 170, 405, 145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.