Highest Common Factor of 8640, 3152 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 8640, 3152 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 8640, 3152 is 16 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 8640, 3152 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 8640, 3152 is 16.
HCF(8640, 3152) = 16
HCF of 8640, 3152 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8640, 3152 is 16.
Highest Common Factor of 8640,3152 is 16
Step 1: Since 8640 > 3152, we apply the division lemma to 8640 and 3152, to get
8640 = 3152 x 2 + 2336
Step 2: Since the reminder 3152 ≠ 0, we apply division lemma to 2336 and 3152, to get
3152 = 2336 x 1 + 816
Step 3: We consider the new divisor 2336 and the new remainder 816, and apply the division lemma to get
2336 = 816 x 2 + 704
We consider the new divisor 816 and the new remainder 704,and apply the division lemma to get
816 = 704 x 1 + 112
We consider the new divisor 704 and the new remainder 112,and apply the division lemma to get
704 = 112 x 6 + 32
We consider the new divisor 112 and the new remainder 32,and apply the division lemma to get
112 = 32 x 3 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 8640 and 3152 is 16
Notice that 16 = HCF(32,16) = HCF(112,32) = HCF(704,112) = HCF(816,704) = HCF(2336,816) = HCF(3152,2336) = HCF(8640,3152) .
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Frequently Asked Questions on HCF of 8640, 3152 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 8640, 3152?
Answer: HCF of 8640, 3152 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8640, 3152 using Euclid's Algorithm?
Answer: For arbitrary numbers 8640, 3152 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.