Question

A number of the form abc,abc always has several prime factors. Which prime
numbers are always factors of a number of this form? Explain why? (Hint: Write in expanded form.)

Answer 1

@jim_thompson5910

Answer 2

@satellite73

Answer 3

@ash2326

Answer 4

abc,abc


100000*a + 10000*b + 1000c + 100*a + 10*b + 1*c


(100000*a + 100*a) + (10000*b + 10*b) + (1000c + 1*c)


100(1000*a + 1*a) + 10(1000*b + 1*b) + 1*(1000c + 1*c)


100(1001*a) + 10(1001*b) + 1*(1001c)


1001*( 100*a + 10*b + 1*c )


7*11*13*( 100*a + 10*b + 1*c )


So this proves that 7, 11, and 13 are always factors of the number abc,abc where 'a','b','c' are positive integers and they are less than 10.

Answer 5

thanks!