Highest Common Factor of 405, 300, 96 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, 300, 96 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 300, 96 is 3 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, 300, 96 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, 300, 96 is 3.
HCF(405, 300, 96) = 3
HCF of 405, 300, 96 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, 300, 96 is 3.
Highest Common Factor of 405,300,96 is 3
Step 1: Since 405 > 300, we apply the division lemma to 405 and 300, to get
405 = 300 x 1 + 105
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 105 and 300, to get
300 = 105 x 2 + 90
Step 3: We consider the new divisor 105 and the new remainder 90, and apply the division lemma to get
105 = 90 x 1 + 15
We consider the new divisor 90 and the new remainder 15, and apply the division lemma to get
90 = 15 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 405 and 300 is 15
Notice that 15 = HCF(90,15) = HCF(105,90) = HCF(300,105) = HCF(405,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 96 > 15, we apply the division lemma to 96 and 15, to get
96 = 15 x 6 + 6
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 6 and 15, to get
15 = 6 x 2 + 3
Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 96 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(96,15) .
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Frequently Asked Questions on HCF of 405, 300, 96 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, 300, 96?
Answer: HCF of 405, 300, 96 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 300, 96 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 300, 96 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.