Highest Common Factor of 405, 465, 140 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 405, 465, 140 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 465, 140 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 405, 465, 140 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 405, 465, 140 is 5.
HCF(405, 465, 140) = 5
HCF of 405, 465, 140 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 405, 465, 140 is 5.
Highest Common Factor of 405,465,140 is 5
Step 1: Since 465 > 405, we apply the division lemma to 465 and 405, to get
465 = 405 x 1 + 60
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 60 and 405, to get
405 = 60 x 6 + 45
Step 3: We consider the new divisor 60 and the new remainder 45, and apply the division lemma to get
60 = 45 x 1 + 15
We consider the new divisor 45 and the new remainder 15, and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 405 and 465 is 15
Notice that 15 = HCF(45,15) = HCF(60,45) = HCF(405,60) = HCF(465,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 140 > 15, we apply the division lemma to 140 and 15, to get
140 = 15 x 9 + 5
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 5 and 15, 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 15 and 140 is 5
Notice that 5 = HCF(15,5) = HCF(140,15) .
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Frequently Asked Questions on HCF of 405, 465, 140 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 405, 465, 140?
Answer: HCF of 405, 465, 140 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 465, 140 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 465, 140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.