How Many Factors?Date: 7/14/96 at 19:6:19 From: PANI BUNDY Subject: How Many Factors? Dear Dr.Math Is there a formula to find the number of factors for a number? For example: The factors of 12 are 12,6,4,3,2,1 ...so there are 6 factors of 12. Do you know what the formula is to find the number of factors for any number? Thank you in advance, Pani Bundy Date: 7/15/96 at 7:37:39 From: Doctor Anthony Subject: Re: How Many Factors? To find the number of factors you must first express the number in prime factors. To take your example, 12 = 2^2 * 3 Now the factor 2 can appear 0, 1 or 2 times (i.e. in 3 different ways) and the factor 3 can occur 0 or 1 times (i.e. in 2 different ways). So the total number of ways the factors can occur is 3 * 2 = 6 ways. So there are 6 possible factors of 12 (including 1 and 12) The general method is to express the number in prime factors, e.g. N = p1^r1 * p2^r2 * p3^r3 Then p1 could occur in r1 + 1 ways p2 could occur in r2 + 1 ways p3 could occur in r3 + 1 ways. Total number of factors = (r1 + 1)(r2 + 1)(r3 + 1) Example. Find the number of possible factors of 144 144 = 2^4 * 3^2 The factor 2 could appear in 5 ways, and the factor 3 in 3 ways, so the total number of factors = 5 * 3 = 15 factors. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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