Highest Common Factor of 8240, 8736 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 8240, 8736 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 8240, 8736 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 8240, 8736 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 8240, 8736 is 16.
HCF(8240, 8736) = 16
HCF of 8240, 8736 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8240, 8736 is 16.
Highest Common Factor of 8240,8736 is 16
Step 1: Since 8736 > 8240, we apply the division lemma to 8736 and 8240, to get
8736 = 8240 x 1 + 496
Step 2: Since the reminder 8240 ≠ 0, we apply division lemma to 496 and 8240, to get
8240 = 496 x 16 + 304
Step 3: We consider the new divisor 496 and the new remainder 304, and apply the division lemma to get
496 = 304 x 1 + 192
We consider the new divisor 304 and the new remainder 192,and apply the division lemma to get
304 = 192 x 1 + 112
We consider the new divisor 192 and the new remainder 112,and apply the division lemma to get
192 = 112 x 1 + 80
We consider the new divisor 112 and the new remainder 80,and apply the division lemma to get
112 = 80 x 1 + 32
We consider the new divisor 80 and the new remainder 32,and apply the division lemma to get
80 = 32 x 2 + 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 8240 and 8736 is 16
Notice that 16 = HCF(32,16) = HCF(80,32) = HCF(112,80) = HCF(192,112) = HCF(304,192) = HCF(496,304) = HCF(8240,496) = HCF(8736,8240) .
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Frequently Asked Questions on HCF of 8240, 8736 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 8240, 8736?
Answer: HCF of 8240, 8736 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8240, 8736 using Euclid's Algorithm?
Answer: For arbitrary numbers 8240, 8736 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.