Highest Common Factor of 723, 9594 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, 9594 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 9594 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, 9594 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, 9594 is 3.
HCF(723, 9594) = 3
HCF of 723, 9594 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, 9594 is 3.
Highest Common Factor of 723,9594 is 3
Step 1: Since 9594 > 723, we apply the division lemma to 9594 and 723, to get
9594 = 723 x 13 + 195
Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 195 and 723, to get
723 = 195 x 3 + 138
Step 3: We consider the new divisor 195 and the new remainder 138, and apply the division lemma to get
195 = 138 x 1 + 57
We consider the new divisor 138 and the new remainder 57,and apply the division lemma to get
138 = 57 x 2 + 24
We consider the new divisor 57 and the new remainder 24,and apply the division lemma to get
57 = 24 x 2 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 723 and 9594 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(57,24) = HCF(138,57) = HCF(195,138) = HCF(723,195) = HCF(9594,723) .
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Frequently Asked Questions on HCF of 723, 9594 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, 9594?
Answer: HCF of 723, 9594 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 9594 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 9594 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.