Highest Common Factor of 103, 7713, 8038 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 103, 7713, 8038 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 103, 7713, 8038 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 103, 7713, 8038 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 103, 7713, 8038 is 1.
HCF(103, 7713, 8038) = 1
HCF of 103, 7713, 8038 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 103, 7713, 8038 is 1.
Highest Common Factor of 103,7713,8038 is 1
Step 1: Since 7713 > 103, we apply the division lemma to 7713 and 103, to get
7713 = 103 x 74 + 91
Step 2: Since the reminder 103 ≠ 0, we apply division lemma to 91 and 103, to get
103 = 91 x 1 + 12
Step 3: We consider the new divisor 91 and the new remainder 12, and apply the division lemma to get
91 = 12 x 7 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 103 and 7713 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(91,12) = HCF(103,91) = HCF(7713,103) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8038 > 1, we apply the division lemma to 8038 and 1, to get
8038 = 1 x 8038 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8038 is 1
Notice that 1 = HCF(8038,1) .
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Frequently Asked Questions on HCF of 103, 7713, 8038 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 103, 7713, 8038?
Answer: HCF of 103, 7713, 8038 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 103, 7713, 8038 using Euclid's Algorithm?
Answer: For arbitrary numbers 103, 7713, 8038 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.