Highest Common Factor of 720, 49542 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 720, 49542 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 49542 is 6 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 720, 49542 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 720, 49542 is 6.
HCF(720, 49542) = 6
HCF of 720, 49542 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 49542 is 6.
Highest Common Factor of 720,49542 is 6
Step 1: Since 49542 > 720, we apply the division lemma to 49542 and 720, to get
49542 = 720 x 68 + 582
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 582 and 720, to get
720 = 582 x 1 + 138
Step 3: We consider the new divisor 582 and the new remainder 138, and apply the division lemma to get
582 = 138 x 4 + 30
We consider the new divisor 138 and the new remainder 30,and apply the division lemma to get
138 = 30 x 4 + 18
We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get
30 = 18 x 1 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 720 and 49542 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(138,30) = HCF(582,138) = HCF(720,582) = HCF(49542,720) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 720, 49542 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 720, 49542?
Answer: HCF of 720, 49542 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 49542 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 49542 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.