Highest Common Factor of 728, 578, 275 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 728, 578, 275 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 578, 275 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 728, 578, 275 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 728, 578, 275 is 1.
HCF(728, 578, 275) = 1
HCF of 728, 578, 275 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 728, 578, 275 is 1.
Highest Common Factor of 728,578,275 is 1
Step 1: Since 728 > 578, we apply the division lemma to 728 and 578, to get
728 = 578 x 1 + 150
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 150 and 578, to get
578 = 150 x 3 + 128
Step 3: We consider the new divisor 150 and the new remainder 128, and apply the division lemma to get
150 = 128 x 1 + 22
We consider the new divisor 128 and the new remainder 22,and apply the division lemma to get
128 = 22 x 5 + 18
We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get
22 = 18 x 1 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 728 and 578 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(128,22) = HCF(150,128) = HCF(578,150) = HCF(728,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 275 > 2, we apply the division lemma to 275 and 2, to get
275 = 2 x 137 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 275 is 1
Notice that 1 = HCF(2,1) = HCF(275,2) .
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Frequently Asked Questions on HCF of 728, 578, 275 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 728, 578, 275?
Answer: HCF of 728, 578, 275 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 578, 275 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 578, 275 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.