Highest Common Factor of 723, 513 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, 513 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 513 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, 513 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, 513 is 3.
HCF(723, 513) = 3
HCF of 723, 513 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, 513 is 3.
Highest Common Factor of 723,513 is 3
Step 1: Since 723 > 513, we apply the division lemma to 723 and 513, to get
723 = 513 x 1 + 210
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 210 and 513, to get
513 = 210 x 2 + 93
Step 3: We consider the new divisor 210 and the new remainder 93, and apply the division lemma to get
210 = 93 x 2 + 24
We consider the new divisor 93 and the new remainder 24,and apply the division lemma to get
93 = 24 x 3 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 723 and 513 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(93,24) = HCF(210,93) = HCF(513,210) = HCF(723,513) .
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Frequently Asked Questions on HCF of 723, 513 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, 513?
Answer: HCF of 723, 513 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 513 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.