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baherus [9]
3 years ago
11

A day can be evenly divided into 86,400 periods of 1 second; 43,200 periods of each 2 seconds; or in many other ways. In total,

how many ways are there to divide a day into periods of seconds, where and are positive integers
Mathematics
1 answer:
Leni [432]3 years ago
7 0

Answer:

96 ways

Step-by-step explanation:

Given

Day = 86400\ seconds

Required

Ways to divide it into period of seconds

What this question implies is to determine the total number of factors of 86400

To start with, we determine the prime factorization of 86400

To do this, we continually divide 86400 by 2; when it can not be further divided, we divide by 3, then 7, then 11...

86400/2 = 43200

43200/2=21600

21600/2=10800

10800/2=5400

5400/2= 2700

2700/2 = 1350

1350/2=675

675/3=225

225/3=75

75/3=25

25/5=5

5/5 = 1

This implies that:

86400 = 2^7 * 3^3 * 5^2

The number of factors d is the solved by:

d = (a+1)*(b+1) *(c+1)

Where

n = 2^a * 3^b * 5^c

By comparison:

a = 7

b = 3

c=2

So:

d = (7+1)*(3+1) *(2+1)

d = 8*4 *3

d = 96

<em>Hence, there are 96 total ways</em>

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\underline{ \text{Given}}:

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