Highest Common Factor of 8123, 754 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, 754 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8123, 754 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, 754 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, 754 is 1.
HCF(8123, 754) = 1
HCF of 8123, 754 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, 754 is 1.
Highest Common Factor of 8123,754 is 1
Step 1: Since 8123 > 754, we apply the division lemma to 8123 and 754, to get
8123 = 754 x 10 + 583
Step 2: Since the reminder 754 ≠ 0, we apply division lemma to 583 and 754, to get
754 = 583 x 1 + 171
Step 3: We consider the new divisor 583 and the new remainder 171, and apply the division lemma to get
583 = 171 x 3 + 70
We consider the new divisor 171 and the new remainder 70,and apply the division lemma to get
171 = 70 x 2 + 31
We consider the new divisor 70 and the new remainder 31,and apply the division lemma to get
70 = 31 x 2 + 8
We consider the new divisor 31 and the new remainder 8,and apply the division lemma to get
31 = 8 x 3 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8123 and 754 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(31,8) = HCF(70,31) = HCF(171,70) = HCF(583,171) = HCF(754,583) = HCF(8123,754) .
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Frequently Asked Questions on HCF of 8123, 754 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, 754?
Answer: HCF of 8123, 754 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8123, 754 using Euclid's Algorithm?
Answer: For arbitrary numbers 8123, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.