Highest Common Factor of 1728, 5342 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 1728, 5342 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1728, 5342 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 1728, 5342 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 1728, 5342 is 2.
HCF(1728, 5342) = 2
HCF of 1728, 5342 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1728, 5342 is 2.
Highest Common Factor of 1728,5342 is 2
Step 1: Since 5342 > 1728, we apply the division lemma to 5342 and 1728, to get
5342 = 1728 x 3 + 158
Step 2: Since the reminder 1728 ≠ 0, we apply division lemma to 158 and 1728, to get
1728 = 158 x 10 + 148
Step 3: We consider the new divisor 158 and the new remainder 148, and apply the division lemma to get
158 = 148 x 1 + 10
We consider the new divisor 148 and the new remainder 10,and apply the division lemma to get
148 = 10 x 14 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1728 and 5342 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(148,10) = HCF(158,148) = HCF(1728,158) = HCF(5342,1728) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1728, 5342 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 1728, 5342?
Answer: HCF of 1728, 5342 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1728, 5342 using Euclid's Algorithm?
Answer: For arbitrary numbers 1728, 5342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
