Highest Common Factor of 8703, 1314 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 8703, 1314 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 8703, 1314 is 9 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 8703, 1314 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 8703, 1314 is 9.
HCF(8703, 1314) = 9
HCF of 8703, 1314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8703, 1314 is 9.
Highest Common Factor of 8703,1314 is 9
Step 1: Since 8703 > 1314, we apply the division lemma to 8703 and 1314, to get
8703 = 1314 x 6 + 819
Step 2: Since the reminder 1314 ≠ 0, we apply division lemma to 819 and 1314, to get
1314 = 819 x 1 + 495
Step 3: We consider the new divisor 819 and the new remainder 495, and apply the division lemma to get
819 = 495 x 1 + 324
We consider the new divisor 495 and the new remainder 324,and apply the division lemma to get
495 = 324 x 1 + 171
We consider the new divisor 324 and the new remainder 171,and apply the division lemma to get
324 = 171 x 1 + 153
We consider the new divisor 171 and the new remainder 153,and apply the division lemma to get
171 = 153 x 1 + 18
We consider the new divisor 153 and the new remainder 18,and apply the division lemma to get
153 = 18 x 8 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 8703 and 1314 is 9
Notice that 9 = HCF(18,9) = HCF(153,18) = HCF(171,153) = HCF(324,171) = HCF(495,324) = HCF(819,495) = HCF(1314,819) = HCF(8703,1314) .
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Frequently Asked Questions on HCF of 8703, 1314 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 8703, 1314?
Answer: HCF of 8703, 1314 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8703, 1314 using Euclid's Algorithm?
Answer: For arbitrary numbers 8703, 1314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.