Highest Common Factor of 7540, 8103 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 7540, 8103 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7540, 8103 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 7540, 8103 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 7540, 8103 is 1.
HCF(7540, 8103) = 1
HCF of 7540, 8103 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7540, 8103 is 1.
Highest Common Factor of 7540,8103 is 1
Step 1: Since 8103 > 7540, we apply the division lemma to 8103 and 7540, to get
8103 = 7540 x 1 + 563
Step 2: Since the reminder 7540 ≠ 0, we apply division lemma to 563 and 7540, to get
7540 = 563 x 13 + 221
Step 3: We consider the new divisor 563 and the new remainder 221, and apply the division lemma to get
563 = 221 x 2 + 121
We consider the new divisor 221 and the new remainder 121,and apply the division lemma to get
221 = 121 x 1 + 100
We consider the new divisor 121 and the new remainder 100,and apply the division lemma to get
121 = 100 x 1 + 21
We consider the new divisor 100 and the new remainder 21,and apply the division lemma to get
100 = 21 x 4 + 16
We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get
21 = 16 x 1 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7540 and 8103 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(100,21) = HCF(121,100) = HCF(221,121) = HCF(563,221) = HCF(7540,563) = HCF(8103,7540) .
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Frequently Asked Questions on HCF of 7540, 8103 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 7540, 8103?
Answer: HCF of 7540, 8103 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7540, 8103 using Euclid's Algorithm?
Answer: For arbitrary numbers 7540, 8103 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.