If N is a positive interger, is the Units digit of N equal to zero?
1) 14 and 35are factors of N
2) N= (2^5) (3^2) (5^7) (7^6)
1) 14 and 35are factors of N
2) N= (2^5) (3^2) (5^7) (7^6)
Units digit of N equal to zero?
1) 14 and 35 are factors of N
=> 14=2*7, 35=7*5
if 14 and 35 are factors of N, then 2,5,7 are factors of N.
if 2 and 5 are both factors of N then 2*5*7*a*b*... will give the last digit as 0, as 2 *5 makes 10 and anything multiplied by 10 gives the last digit as 0
sufficient
2)N= (2^5) (3^2) (5^7) (7^6)
=> N= (2*5)^5*(3^2)*(7^6)*(5^2)
=> N=10^5 *(3^2)*(7^6)*(5^2)
will give the last digit as 0 as powers of 10 multiplied by any number will give 0 as the last digit
sufficient
hence D
