Highest Common Factor of 752, 542 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 752, 542 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 752, 542 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 752, 542 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 752, 542 is 2.
HCF(752, 542) = 2
HCF of 752, 542 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 752, 542 is 2.
Highest Common Factor of 752,542 is 2
Step 1: Since 752 > 542, we apply the division lemma to 752 and 542, to get
752 = 542 x 1 + 210
Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 210 and 542, to get
542 = 210 x 2 + 122
Step 3: We consider the new divisor 210 and the new remainder 122, and apply the division lemma to get
210 = 122 x 1 + 88
We consider the new divisor 122 and the new remainder 88,and apply the division lemma to get
122 = 88 x 1 + 34
We consider the new divisor 88 and the new remainder 34,and apply the division lemma to get
88 = 34 x 2 + 20
We consider the new divisor 34 and the new remainder 20,and apply the division lemma to get
34 = 20 x 1 + 14
We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 752 and 542 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(34,20) = HCF(88,34) = HCF(122,88) = HCF(210,122) = HCF(542,210) = HCF(752,542) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 752, 542 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 752, 542?
Answer: HCF of 752, 542 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 752, 542 using Euclid's Algorithm?
Answer: For arbitrary numbers 752, 542 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.