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# How many prime numbers between 1 and 100 are factors of

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Senior Manager
Joined: 08 Jun 2004
Posts: 495
Location: Europe
How many prime numbers between 1 and 100 are factors of [#permalink]

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30 Apr 2006, 08:12
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How many prime numbers between 1 and 100 are factors of 7,150 ?

A. One
B. Two
C. Three
D. Four
E. Five

VP
Joined: 28 Mar 2006
Posts: 1369
Re: PS: Factors of 7,150? [#permalink]

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30 Apr 2006, 09:30
M8 wrote:
How many prime numbers between 1 and 100 are factors of 7,150 ?

A. One
B. Two
C. Three
D. Four
E. Five

Factorize it and get 4 unique factors
2*5*5*11*13
Manager
Joined: 20 Nov 2004
Posts: 108
Re: PS: Factors of 7,150? [#permalink]

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30 Apr 2006, 09:31
First, find the prime factorization of 7150. I fear there is
no shortcut for that

7150 = 2 * 5^2 * 11 * 13

That's it. You don't have to check any combinations because
the numbers couldn't be prime.

So 2, 5, 11 and 13 and therefore D.

By the way, the condition "between 1 and 100" is useless.
VP
Joined: 28 Mar 2006
Posts: 1369
Re: PS: Factors of 7,150? [#permalink]

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30 Apr 2006, 09:33
ccax wrote:
First, find the prime factorization of 7150. I fear there is
no shortcut for that

7150 = 2 * 5^2 * 11 * 13

That's it. You don't have to check any combinations because
the numbers couldn't be prime.

So 2, 5, 11 and 13 and therefore D.

By the way, the condition "between 1 and 100" is useless.

its handy to have the mulitplication tables by heart....Tough to do it...But it does pay back
Manager
Joined: 14 Mar 2006
Posts: 208
Re: PS: Factors of 7,150? [#permalink]

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30 Apr 2006, 19:49
trivikram wrote:
M8 wrote:
How many prime numbers between 1 and 100 are factors of 7,150 ?

A. One
B. Two
C. Three
D. Four
E. Five

Factorize it and get 4 unique factors
2*5*5*11*13

btw, is there a shortcut to know if a number is divisible by 11 and/or 13? In this case 143 is divisible by both. Thanks
VP
Joined: 28 Mar 2006
Posts: 1369
Re: PS: Factors of 7,150? [#permalink]

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30 Apr 2006, 19:59
shampoo wrote:
trivikram wrote:
M8 wrote:
How many prime numbers between 1 and 100 are factors of 7,150 ?

A. One
B. Two
C. Three
D. Four
E. Five

Factorize it and get 4 unique factors
2*5*5*11*13

btw, is there a shortcut to know if a number is divisible by 11 and/or 13? In this case 143 is divisible by both. Thanks

143 is divisble by 11

Add alternate numbers and subtract one from the other

1+3 = 4
the other alterrnate number is 4
So 4-4 = 0 is divisible by 11

So this is a test for 11 divisibility
Senior Manager
Joined: 08 Jun 2004
Posts: 495
Location: Europe

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01 May 2006, 01:43
OA is 'D' (Four)
Great work guys.
01 May 2006, 01:43
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