Highest Common Factor of 728, 878, 928 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, 878, 928 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 878, 928 is 2 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, 878, 928 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, 878, 928 is 2.
HCF(728, 878, 928) = 2
HCF of 728, 878, 928 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, 878, 928 is 2.
Highest Common Factor of 728,878,928 is 2
Step 1: Since 878 > 728, we apply the division lemma to 878 and 728, to get
878 = 728 x 1 + 150
Step 2: Since the reminder 728 ≠ 0, we apply division lemma to 150 and 728, to get
728 = 150 x 4 + 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 878 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(128,22) = HCF(150,128) = HCF(728,150) = HCF(878,728) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 928 > 2, we apply the division lemma to 928 and 2, to get
928 = 2 x 464 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 928 is 2
Notice that 2 = HCF(928,2) .
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Frequently Asked Questions on HCF of 728, 878, 928 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, 878, 928?
Answer: HCF of 728, 878, 928 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 878, 928 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 878, 928 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
