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, 15558 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 15558 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, 15558 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, 15558 is 2.
HCF(728, 15558) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 728, 15558 is 2.
Step 1: Since 15558 > 728, we apply the division lemma to 15558 and 728, to get
15558 = 728 x 21 + 270
Step 2: Since the reminder 728 ≠ 0, we apply division lemma to 270 and 728, to get
728 = 270 x 2 + 188
Step 3: We consider the new divisor 270 and the new remainder 188, and apply the division lemma to get
270 = 188 x 1 + 82
We consider the new divisor 188 and the new remainder 82,and apply the division lemma to get
188 = 82 x 2 + 24
We consider the new divisor 82 and the new remainder 24,and apply the division lemma to get
82 = 24 x 3 + 10
We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 15558 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(82,24) = HCF(188,82) = HCF(270,188) = HCF(728,270) = HCF(15558,728) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 15558?
Answer: HCF of 728, 15558 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 15558 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 15558 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.