Highest Common Factor of 405, 315, 460 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, 315, 460 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 315, 460 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, 315, 460 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, 315, 460 is 5.
HCF(405, 315, 460) = 5
HCF of 405, 315, 460 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, 315, 460 is 5.
Highest Common Factor of 405,315,460 is 5
Step 1: Since 405 > 315, we apply the division lemma to 405 and 315, to get
405 = 315 x 1 + 90
Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 90 and 315, to get
315 = 90 x 3 + 45
Step 3: We consider the new divisor 90 and the new remainder 45, and apply the division lemma to get
90 = 45 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 405 and 315 is 45
Notice that 45 = HCF(90,45) = HCF(315,90) = HCF(405,315) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 460 > 45, we apply the division lemma to 460 and 45, to get
460 = 45 x 10 + 10
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 10 and 45, to get
45 = 10 x 4 + 5
Step 3: 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 45 and 460 is 5
Notice that 5 = HCF(10,5) = HCF(45,10) = HCF(460,45) .
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Frequently Asked Questions on HCF of 405, 315, 460 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, 315, 460?
Answer: HCF of 405, 315, 460 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 315, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 315, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.