Highest Common Factor of 8042, 7131 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 8042, 7131 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8042, 7131 is 1 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 8042, 7131 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 8042, 7131 is 1.
HCF(8042, 7131) = 1
HCF of 8042, 7131 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8042, 7131 is 1.
Highest Common Factor of 8042,7131 is 1
Step 1: Since 8042 > 7131, we apply the division lemma to 8042 and 7131, to get
8042 = 7131 x 1 + 911
Step 2: Since the reminder 7131 ≠ 0, we apply division lemma to 911 and 7131, to get
7131 = 911 x 7 + 754
Step 3: We consider the new divisor 911 and the new remainder 754, and apply the division lemma to get
911 = 754 x 1 + 157
We consider the new divisor 754 and the new remainder 157,and apply the division lemma to get
754 = 157 x 4 + 126
We consider the new divisor 157 and the new remainder 126,and apply the division lemma to get
157 = 126 x 1 + 31
We consider the new divisor 126 and the new remainder 31,and apply the division lemma to get
126 = 31 x 4 + 2
We consider the new divisor 31 and the new remainder 2,and apply the division lemma to get
31 = 2 x 15 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8042 and 7131 is 1
Notice that 1 = HCF(2,1) = HCF(31,2) = HCF(126,31) = HCF(157,126) = HCF(754,157) = HCF(911,754) = HCF(7131,911) = HCF(8042,7131) .
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Frequently Asked Questions on HCF of 8042, 7131 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 8042, 7131?
Answer: HCF of 8042, 7131 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8042, 7131 using Euclid's Algorithm?
Answer: For arbitrary numbers 8042, 7131 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.