Highest Common Factor of 8272, 7984, 18656 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 8272, 7984, 18656 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 8272, 7984, 18656 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 8272, 7984, 18656 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 8272, 7984, 18656 is 16.
HCF(8272, 7984, 18656) = 16
HCF of 8272, 7984, 18656 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8272, 7984, 18656 is 16.
Highest Common Factor of 8272,7984,18656 is 16
Step 1: Since 8272 > 7984, we apply the division lemma to 8272 and 7984, to get
8272 = 7984 x 1 + 288
Step 2: Since the reminder 7984 ≠ 0, we apply division lemma to 288 and 7984, to get
7984 = 288 x 27 + 208
Step 3: We consider the new divisor 288 and the new remainder 208, and apply the division lemma to get
288 = 208 x 1 + 80
We consider the new divisor 208 and the new remainder 80,and apply the division lemma to get
208 = 80 x 2 + 48
We consider the new divisor 80 and the new remainder 48,and apply the division lemma to get
80 = 48 x 1 + 32
We consider the new divisor 48 and the new remainder 32,and apply the division lemma to get
48 = 32 x 1 + 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 8272 and 7984 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(80,48) = HCF(208,80) = HCF(288,208) = HCF(7984,288) = HCF(8272,7984) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 18656 > 16, we apply the division lemma to 18656 and 16, to get
18656 = 16 x 1166 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 16 and 18656 is 16
Notice that 16 = HCF(18656,16) .
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Frequently Asked Questions on HCF of 8272, 7984, 18656 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 8272, 7984, 18656?
Answer: HCF of 8272, 7984, 18656 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8272, 7984, 18656 using Euclid's Algorithm?
Answer: For arbitrary numbers 8272, 7984, 18656 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
