Highest Common Factor of 8724, 9145 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 8724, 9145 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8724, 9145 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 8724, 9145 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 8724, 9145 is 1.
HCF(8724, 9145) = 1
HCF of 8724, 9145 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8724, 9145 is 1.
Highest Common Factor of 8724,9145 is 1
Step 1: Since 9145 > 8724, we apply the division lemma to 9145 and 8724, to get
9145 = 8724 x 1 + 421
Step 2: Since the reminder 8724 ≠ 0, we apply division lemma to 421 and 8724, to get
8724 = 421 x 20 + 304
Step 3: We consider the new divisor 421 and the new remainder 304, and apply the division lemma to get
421 = 304 x 1 + 117
We consider the new divisor 304 and the new remainder 117,and apply the division lemma to get
304 = 117 x 2 + 70
We consider the new divisor 117 and the new remainder 70,and apply the division lemma to get
117 = 70 x 1 + 47
We consider the new divisor 70 and the new remainder 47,and apply the division lemma to get
70 = 47 x 1 + 23
We consider the new divisor 47 and the new remainder 23,and apply the division lemma to get
47 = 23 x 2 + 1
We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8724 and 9145 is 1
Notice that 1 = HCF(23,1) = HCF(47,23) = HCF(70,47) = HCF(117,70) = HCF(304,117) = HCF(421,304) = HCF(8724,421) = HCF(9145,8724) .
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Frequently Asked Questions on HCF of 8724, 9145 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 8724, 9145?
Answer: HCF of 8724, 9145 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8724, 9145 using Euclid's Algorithm?
Answer: For arbitrary numbers 8724, 9145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
