Highest Common Factor of 8123, 5701 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 8123, 5701 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8123, 5701 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 8123, 5701 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 8123, 5701 is 1.
HCF(8123, 5701) = 1
HCF of 8123, 5701 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8123, 5701 is 1.
Highest Common Factor of 8123,5701 is 1
Step 1: Since 8123 > 5701, we apply the division lemma to 8123 and 5701, to get
8123 = 5701 x 1 + 2422
Step 2: Since the reminder 5701 ≠ 0, we apply division lemma to 2422 and 5701, to get
5701 = 2422 x 2 + 857
Step 3: We consider the new divisor 2422 and the new remainder 857, and apply the division lemma to get
2422 = 857 x 2 + 708
We consider the new divisor 857 and the new remainder 708,and apply the division lemma to get
857 = 708 x 1 + 149
We consider the new divisor 708 and the new remainder 149,and apply the division lemma to get
708 = 149 x 4 + 112
We consider the new divisor 149 and the new remainder 112,and apply the division lemma to get
149 = 112 x 1 + 37
We consider the new divisor 112 and the new remainder 37,and apply the division lemma to get
112 = 37 x 3 + 1
We consider the new divisor 37 and the new remainder 1,and apply the division lemma to get
37 = 1 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8123 and 5701 is 1
Notice that 1 = HCF(37,1) = HCF(112,37) = HCF(149,112) = HCF(708,149) = HCF(857,708) = HCF(2422,857) = HCF(5701,2422) = HCF(8123,5701) .
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Frequently Asked Questions on HCF of 8123, 5701 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 8123, 5701?
Answer: HCF of 8123, 5701 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8123, 5701 using Euclid's Algorithm?
Answer: For arbitrary numbers 8123, 5701 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.