Highest Common Factor of 723, 996 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, 996 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 996 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, 996 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, 996 is 3.
HCF(723, 996) = 3
HCF of 723, 996 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, 996 is 3.
Highest Common Factor of 723,996 is 3
Step 1: Since 996 > 723, we apply the division lemma to 996 and 723, to get
996 = 723 x 1 + 273
Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 273 and 723, to get
723 = 273 x 2 + 177
Step 3: We consider the new divisor 273 and the new remainder 177, and apply the division lemma to get
273 = 177 x 1 + 96
We consider the new divisor 177 and the new remainder 96,and apply the division lemma to get
177 = 96 x 1 + 81
We consider the new divisor 96 and the new remainder 81,and apply the division lemma to get
96 = 81 x 1 + 15
We consider the new divisor 81 and the new remainder 15,and apply the division lemma to get
81 = 15 x 5 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 996 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(81,15) = HCF(96,81) = HCF(177,96) = HCF(273,177) = HCF(723,273) = HCF(996,723) .
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Frequently Asked Questions on HCF of 723, 996 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, 996?
Answer: HCF of 723, 996 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 996 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.