shahab1987 wrote:

Hi, i think that 25 could not be a factor of 20! because it is 5*5 but we have just one 5, am i right?

No.. we have four 5 in 20! as 20! = 1*2*3*4*5*6..*10*11*...15*16..*20, so one five comes from each of 5, 10, 15 and 20. so \(5^4\)

Which of the following is NOT a factor of 20! ?

A. 17.......\(20!=1*2*.....17*...20\).. YES

B. 21=3*7.......\(20!=1*2*3.....7*...20\).. YES

C. 25=5*5.......\(20!=1*2*...*5*..10*.....*15*....20\).. YES

D. 29.... since 29 is a PRIME number and 20! contains number only till 20, 29 will NOT be there in 20!

E. 42=2*3*7.......\(20!=1*2*3*.....7*...20\).. YES

F. 51=3*17.......\(20!=1*2*3.....17*...20\).. YES

G. 85=5*17.......\(20!=1*2*3*4*5*.....17*...20\).. YES

H. 121=11*11...........\(20!=1*2*.....11*...20\).. NO, as we have only one 11.

so D and H

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Some useful Theory.

1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html