Highest Common Factor of 723, 405 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 723, 405 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 405 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 723, 405 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 723, 405 is 3.
HCF(723, 405) = 3
HCF of 723, 405 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 723, 405 is 3.
Highest Common Factor of 723,405 is 3
Step 1: Since 723 > 405, we apply the division lemma to 723 and 405, to get
723 = 405 x 1 + 318
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 318 and 405, to get
405 = 318 x 1 + 87
Step 3: We consider the new divisor 318 and the new remainder 87, and apply the division lemma to get
318 = 87 x 3 + 57
We consider the new divisor 87 and the new remainder 57,and apply the division lemma to get
87 = 57 x 1 + 30
We consider the new divisor 57 and the new remainder 30,and apply the division lemma to get
57 = 30 x 1 + 27
We consider the new divisor 30 and the new remainder 27,and apply the division lemma to get
30 = 27 x 1 + 3
We consider the new divisor 27 and the new remainder 3,and apply the division lemma to get
27 = 3 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 723 and 405 is 3
Notice that 3 = HCF(27,3) = HCF(30,27) = HCF(57,30) = HCF(87,57) = HCF(318,87) = HCF(405,318) = HCF(723,405) .
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Frequently Asked Questions on HCF of 723, 405 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 723, 405?
Answer: HCF of 723, 405 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 405 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.