Highest Common Factor of 1566, 9968, 32960 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 1566, 9968, 32960 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1566, 9968, 32960 is 2 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 1566, 9968, 32960 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 1566, 9968, 32960 is 2.
HCF(1566, 9968, 32960) = 2
HCF of 1566, 9968, 32960 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1566, 9968, 32960 is 2.
Highest Common Factor of 1566,9968,32960 is 2
Step 1: Since 9968 > 1566, we apply the division lemma to 9968 and 1566, to get
9968 = 1566 x 6 + 572
Step 2: Since the reminder 1566 ≠ 0, we apply division lemma to 572 and 1566, to get
1566 = 572 x 2 + 422
Step 3: We consider the new divisor 572 and the new remainder 422, and apply the division lemma to get
572 = 422 x 1 + 150
We consider the new divisor 422 and the new remainder 150,and apply the division lemma to get
422 = 150 x 2 + 122
We consider the new divisor 150 and the new remainder 122,and apply the division lemma to get
150 = 122 x 1 + 28
We consider the new divisor 122 and the new remainder 28,and apply the division lemma to get
122 = 28 x 4 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1566 and 9968 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(122,28) = HCF(150,122) = HCF(422,150) = HCF(572,422) = HCF(1566,572) = HCF(9968,1566) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32960 > 2, we apply the division lemma to 32960 and 2, to get
32960 = 2 x 16480 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 32960 is 2
Notice that 2 = HCF(32960,2) .
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Frequently Asked Questions on HCF of 1566, 9968, 32960 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 1566, 9968, 32960?
Answer: HCF of 1566, 9968, 32960 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1566, 9968, 32960 using Euclid's Algorithm?
Answer: For arbitrary numbers 1566, 9968, 32960 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.