Highest Common Factor of 9055, 8174 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 9055, 8174 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9055, 8174 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 9055, 8174 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 9055, 8174 is 1.
HCF(9055, 8174) = 1
HCF of 9055, 8174 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9055, 8174 is 1.
Highest Common Factor of 9055,8174 is 1
Step 1: Since 9055 > 8174, we apply the division lemma to 9055 and 8174, to get
9055 = 8174 x 1 + 881
Step 2: Since the reminder 8174 ≠ 0, we apply division lemma to 881 and 8174, to get
8174 = 881 x 9 + 245
Step 3: We consider the new divisor 881 and the new remainder 245, and apply the division lemma to get
881 = 245 x 3 + 146
We consider the new divisor 245 and the new remainder 146,and apply the division lemma to get
245 = 146 x 1 + 99
We consider the new divisor 146 and the new remainder 99,and apply the division lemma to get
146 = 99 x 1 + 47
We consider the new divisor 99 and the new remainder 47,and apply the division lemma to get
99 = 47 x 2 + 5
We consider the new divisor 47 and the new remainder 5,and apply the division lemma to get
47 = 5 x 9 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 9055 and 8174 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(47,5) = HCF(99,47) = HCF(146,99) = HCF(245,146) = HCF(881,245) = HCF(8174,881) = HCF(9055,8174) .
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Frequently Asked Questions on HCF of 9055, 8174 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 9055, 8174?
Answer: HCF of 9055, 8174 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9055, 8174 using Euclid's Algorithm?
Answer: For arbitrary numbers 9055, 8174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.