Highest Common Factor of 5872, 9576 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 5872, 9576 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 5872, 9576 is 8 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 5872, 9576 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 5872, 9576 is 8.
HCF(5872, 9576) = 8
HCF of 5872, 9576 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5872, 9576 is 8.
Highest Common Factor of 5872,9576 is 8
Step 1: Since 9576 > 5872, we apply the division lemma to 9576 and 5872, to get
9576 = 5872 x 1 + 3704
Step 2: Since the reminder 5872 ≠ 0, we apply division lemma to 3704 and 5872, to get
5872 = 3704 x 1 + 2168
Step 3: We consider the new divisor 3704 and the new remainder 2168, and apply the division lemma to get
3704 = 2168 x 1 + 1536
We consider the new divisor 2168 and the new remainder 1536,and apply the division lemma to get
2168 = 1536 x 1 + 632
We consider the new divisor 1536 and the new remainder 632,and apply the division lemma to get
1536 = 632 x 2 + 272
We consider the new divisor 632 and the new remainder 272,and apply the division lemma to get
632 = 272 x 2 + 88
We consider the new divisor 272 and the new remainder 88,and apply the division lemma to get
272 = 88 x 3 + 8
We consider the new divisor 88 and the new remainder 8,and apply the division lemma to get
88 = 8 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 5872 and 9576 is 8
Notice that 8 = HCF(88,8) = HCF(272,88) = HCF(632,272) = HCF(1536,632) = HCF(2168,1536) = HCF(3704,2168) = HCF(5872,3704) = HCF(9576,5872) .
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Frequently Asked Questions on HCF of 5872, 9576 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 5872, 9576?
Answer: HCF of 5872, 9576 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5872, 9576 using Euclid's Algorithm?
Answer: For arbitrary numbers 5872, 9576 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.