JMark
  • JMark
Hi can you please help me to solve this prob? Find the number divisors of 240
Mathematics
chestercat
  • chestercat
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AlexandervonHumboldt2
  • AlexandervonHumboldt2
the first divisor is 2: 240/2=120 120/2=60 60/2=30 30/2=15 15/3=5 5/5=1 each time you divide new number by the it's smallest divisor: thus your divisors are 2, 4, 8, 16, 6, 10, 48, 30, 15, 60, 5, 120, 240, 1, 3, 80 , 24, 12, 20, 40, that's all if i didn't forgot anything prime factorization is 2*2*2*2*3*5
AlexandervonHumboldt2
  • AlexandervonHumboldt2
to find divisors of 240, first write it's prime factorization, then calculate all of the combinations between the prime factors
AlexandervonHumboldt2
  • AlexandervonHumboldt2

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mom.
  • mom.
what kind of divisors? 2.4 is also a divisor :)
mathmath333
  • mathmath333
is the answer 20
ganeshie8
  • ganeshie8
\(240 = 2^4*3*5\) So, any divisor of \(240\) will be of form \(2^a*3^b*5^c\), where \(0\le a\le 4\) and \(~0\le b,c\le 1\)
AlexandervonHumboldt2
  • AlexandervonHumboldt2
yeah gane is right
mathmath333
  • mathmath333
mom=Mars Orbiter Mission
mom.
  • mom.
mom=mother of mankind (;
ganeshie8
  • ganeshie8
Notice that we can choose the exponent \(a\) in \(5\) ways, \(b\) in \(2\) ways, \(c\) in \(2\) ways therefore total number of positive divisors = \(5*2*2=20\)
mathmath333
  • mathmath333
i learnt this stuff 1 year ago here now i forgot it
mom.
  • mom.
same
AlexandervonHumboldt2
  • AlexandervonHumboldt2
looks like Mister.Mark is not in a hurry to see our explanations @JMark
mathmath333
  • mathmath333
i just remembered the pattern (a+1)(b+1)(c+1)....=no of divisors
mom.
  • mom.
looks like he did it himself (;

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