Highest Common Factor of 8306, 8003 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 8306, 8003 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8306, 8003 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 8306, 8003 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 8306, 8003 is 1.
HCF(8306, 8003) = 1
HCF of 8306, 8003 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8306, 8003 is 1.
Highest Common Factor of 8306,8003 is 1
Step 1: Since 8306 > 8003, we apply the division lemma to 8306 and 8003, to get
8306 = 8003 x 1 + 303
Step 2: Since the reminder 8003 ≠ 0, we apply division lemma to 303 and 8003, to get
8003 = 303 x 26 + 125
Step 3: We consider the new divisor 303 and the new remainder 125, and apply the division lemma to get
303 = 125 x 2 + 53
We consider the new divisor 125 and the new remainder 53,and apply the division lemma to get
125 = 53 x 2 + 19
We consider the new divisor 53 and the new remainder 19,and apply the division lemma to get
53 = 19 x 2 + 15
We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get
19 = 15 x 1 + 4
We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get
15 = 4 x 3 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8306 and 8003 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(53,19) = HCF(125,53) = HCF(303,125) = HCF(8003,303) = HCF(8306,8003) .
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Frequently Asked Questions on HCF of 8306, 8003 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 8306, 8003?
Answer: HCF of 8306, 8003 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8306, 8003 using Euclid's Algorithm?
Answer: For arbitrary numbers 8306, 8003 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.