Highest Common Factor of 810, 252, 723 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 810, 252, 723 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 810, 252, 723 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 810, 252, 723 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 810, 252, 723 is 3.
HCF(810, 252, 723) = 3
HCF of 810, 252, 723 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 810, 252, 723 is 3.
Highest Common Factor of 810,252,723 is 3
Step 1: Since 810 > 252, we apply the division lemma to 810 and 252, to get
810 = 252 x 3 + 54
Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 54 and 252, to get
252 = 54 x 4 + 36
Step 3: We consider the new divisor 54 and the new remainder 36, and apply the division lemma to get
54 = 36 x 1 + 18
We consider the new divisor 36 and the new remainder 18, and apply the division lemma to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 810 and 252 is 18
Notice that 18 = HCF(36,18) = HCF(54,36) = HCF(252,54) = HCF(810,252) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 723 > 18, we apply the division lemma to 723 and 18, to get
723 = 18 x 40 + 3
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 3 and 18, to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 18 and 723 is 3
Notice that 3 = HCF(18,3) = HCF(723,18) .
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Frequently Asked Questions on HCF of 810, 252, 723 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 810, 252, 723?
Answer: HCF of 810, 252, 723 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 810, 252, 723 using Euclid's Algorithm?
Answer: For arbitrary numbers 810, 252, 723 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.