Highest Common Factor of 723, 984, 827 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, 984, 827 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 984, 827 is 1 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, 984, 827 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, 984, 827 is 1.
HCF(723, 984, 827) = 1
HCF of 723, 984, 827 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, 984, 827 is 1.
Highest Common Factor of 723,984,827 is 1
Step 1: Since 984 > 723, we apply the division lemma to 984 and 723, to get
984 = 723 x 1 + 261
Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 261 and 723, to get
723 = 261 x 2 + 201
Step 3: We consider the new divisor 261 and the new remainder 201, and apply the division lemma to get
261 = 201 x 1 + 60
We consider the new divisor 201 and the new remainder 60,and apply the division lemma to get
201 = 60 x 3 + 21
We consider the new divisor 60 and the new remainder 21,and apply the division lemma to get
60 = 21 x 2 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma 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 723 and 984 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(60,21) = HCF(201,60) = HCF(261,201) = HCF(723,261) = HCF(984,723) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 827 > 3, we apply the division lemma to 827 and 3, to get
827 = 3 x 275 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 827 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(827,3) .
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Frequently Asked Questions on HCF of 723, 984, 827 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, 984, 827?
Answer: HCF of 723, 984, 827 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 984, 827 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 984, 827 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.