Highest Common Factor of 723, 441, 978 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, 441, 978 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 441, 978 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, 441, 978 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, 441, 978 is 3.
HCF(723, 441, 978) = 3
HCF of 723, 441, 978 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, 441, 978 is 3.
Highest Common Factor of 723,441,978 is 3
Step 1: Since 723 > 441, we apply the division lemma to 723 and 441, to get
723 = 441 x 1 + 282
Step 2: Since the reminder 441 ≠ 0, we apply division lemma to 282 and 441, to get
441 = 282 x 1 + 159
Step 3: We consider the new divisor 282 and the new remainder 159, and apply the division lemma to get
282 = 159 x 1 + 123
We consider the new divisor 159 and the new remainder 123,and apply the division lemma to get
159 = 123 x 1 + 36
We consider the new divisor 123 and the new remainder 36,and apply the division lemma to get
123 = 36 x 3 + 15
We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get
36 = 15 x 2 + 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 441 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(123,36) = HCF(159,123) = HCF(282,159) = HCF(441,282) = HCF(723,441) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 3, we apply the division lemma to 978 and 3, to get
978 = 3 x 326 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 978 is 3
Notice that 3 = HCF(978,3) .
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Frequently Asked Questions on HCF of 723, 441, 978 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, 441, 978?
Answer: HCF of 723, 441, 978 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 441, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 441, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.