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Sphenic Numbers. How to identify if a number is sphenic or not spenic.

Updated on June 18, 2013

A sphenic number is a positive whole number that can be written as product of three distinct prime factors. So in order decide if a number is a sphenic number or not follow these two simple steps:

Step 1 Work out the product of prime factors for the number you are checking.

Step 2 If the product of prime factors contains 3 distinct prime factors then the number will be sphenic. If not then the number will not be sphenic.

Example 1

Is the number 42 a sphenic number? Explain your answer.

First work out the product of the product of prime factors:

42/2 = 21

21/3 = 7

So 2 × 3 × 7 = 42

Since there are 3 prime factors and all are distinct then 42 is a sphenic number.

Example 2

Is the number 18 a sphenic number? Explain your answer.

First work out the product of the product of prime factors:

18/2 = 9

9/3 = 3

So 2 × 3 × 3 = 18

18 is not a sphenic number as there are not 3 distinct prime factors.

Example 3

Is the number 78 a sphenic number? Explain your answer.

First work out the product of the product of prime factors:

78/2 = 39

39/3 = 13

So 2 × 3 × 13 = 78

Since there are 3 prime factors and all are distinct then 78 is a sphenic number.

Example 4

Is the number 210 a sphenic number? Explain your answer.

First work out the product of the product of prime factors:

210/2 = 105

105/3 = 35

35/5 = 7

So 2 × 3 × 5 × 7 = 210

210 is not a sphenic number as there are 4 distinct prime factors not 3.

Example 5

Is the number 110 a sphenic number? Explain your answer.

First work out the product of the product of prime factors:

110/2 = 55

55/5 = 11

So 2 × 5 × 11 = 110

Since there are 3 prime factors and all are distinct then 110 is a sphenic number.

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