Highest Common Factor of 8409, 184 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 8409, 184 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8409, 184 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 8409, 184 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 8409, 184 is 1.
HCF(8409, 184) = 1
HCF of 8409, 184 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8409, 184 is 1.
Highest Common Factor of 8409,184 is 1
Step 1: Since 8409 > 184, we apply the division lemma to 8409 and 184, to get
8409 = 184 x 45 + 129
Step 2: Since the reminder 184 ≠ 0, we apply division lemma to 129 and 184, to get
184 = 129 x 1 + 55
Step 3: We consider the new divisor 129 and the new remainder 55, and apply the division lemma to get
129 = 55 x 2 + 19
We consider the new divisor 55 and the new remainder 19,and apply the division lemma to get
55 = 19 x 2 + 17
We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get
19 = 17 x 1 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 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 8409 and 184 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(55,19) = HCF(129,55) = HCF(184,129) = HCF(8409,184) .
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Frequently Asked Questions on HCF of 8409, 184 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 8409, 184?
Answer: HCF of 8409, 184 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8409, 184 using Euclid's Algorithm?
Answer: For arbitrary numbers 8409, 184 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
