Highest Common Factor of 5460, 7742 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 5460, 7742 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 5460, 7742 is 14 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 5460, 7742 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 5460, 7742 is 14.
HCF(5460, 7742) = 14
HCF of 5460, 7742 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5460, 7742 is 14.
Highest Common Factor of 5460,7742 is 14
Step 1: Since 7742 > 5460, we apply the division lemma to 7742 and 5460, to get
7742 = 5460 x 1 + 2282
Step 2: Since the reminder 5460 ≠ 0, we apply division lemma to 2282 and 5460, to get
5460 = 2282 x 2 + 896
Step 3: We consider the new divisor 2282 and the new remainder 896, and apply the division lemma to get
2282 = 896 x 2 + 490
We consider the new divisor 896 and the new remainder 490,and apply the division lemma to get
896 = 490 x 1 + 406
We consider the new divisor 490 and the new remainder 406,and apply the division lemma to get
490 = 406 x 1 + 84
We consider the new divisor 406 and the new remainder 84,and apply the division lemma to get
406 = 84 x 4 + 70
We consider the new divisor 84 and the new remainder 70,and apply the division lemma to get
84 = 70 x 1 + 14
We consider the new divisor 70 and the new remainder 14,and apply the division lemma to get
70 = 14 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 5460 and 7742 is 14
Notice that 14 = HCF(70,14) = HCF(84,70) = HCF(406,84) = HCF(490,406) = HCF(896,490) = HCF(2282,896) = HCF(5460,2282) = HCF(7742,5460) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 5460, 7742 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 5460, 7742?
Answer: HCF of 5460, 7742 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5460, 7742 using Euclid's Algorithm?
Answer: For arbitrary numbers 5460, 7742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.