Highest Common Factor of 7138, 8242 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 7138, 8242 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7138, 8242 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 7138, 8242 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 7138, 8242 is 2.
HCF(7138, 8242) = 2
HCF of 7138, 8242 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7138, 8242 is 2.
Highest Common Factor of 7138,8242 is 2
Step 1: Since 8242 > 7138, we apply the division lemma to 8242 and 7138, to get
8242 = 7138 x 1 + 1104
Step 2: Since the reminder 7138 ≠ 0, we apply division lemma to 1104 and 7138, to get
7138 = 1104 x 6 + 514
Step 3: We consider the new divisor 1104 and the new remainder 514, and apply the division lemma to get
1104 = 514 x 2 + 76
We consider the new divisor 514 and the new remainder 76,and apply the division lemma to get
514 = 76 x 6 + 58
We consider the new divisor 76 and the new remainder 58,and apply the division lemma to get
76 = 58 x 1 + 18
We consider the new divisor 58 and the new remainder 18,and apply the division lemma to get
58 = 18 x 3 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 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 7138 and 8242 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(58,18) = HCF(76,58) = HCF(514,76) = HCF(1104,514) = HCF(7138,1104) = HCF(8242,7138) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 7138, 8242 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 7138, 8242?
Answer: HCF of 7138, 8242 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7138, 8242 using Euclid's Algorithm?
Answer: For arbitrary numbers 7138, 8242 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.