## TinaSh one year ago A mathematician states that her children’s ages are all prime numbers that multiply together to give 7,429. She also says that two of her children are teenagers. What are her children s age?

1. freckles

so we have $a \cdot b \cdot c=7429$

2. freckles

we know prime numbers are odd for the most part

3. freckles

and we know 7429 is not even so none of the primes are 2

4. freckles

two of her children are teenagers so they could be 13,17, or 19

5. freckles

I would probably try to write the prime factorization of 7429

6. freckles

can you do that?

7. TinaSh

wait what are prime numbers? :\$

8. freckles

prime numbers are integers that are only divisible by themselves and 1.

9. freckles

the key here is just to write 7429 in prime factorization that is all there is to the problem

10. freckles

like for example 25=5*5 or 5^2 31 is prime 25 was not umm... 2 is the only even prime

11. TinaSh

I dont even know what factorization means >.< I missed few days of school.

12. campbell_st

one tip... given the last digit is 9... I'd divide the original number by 17

13. freckles

example: the prime factorization of 12=2*2*3

14. TinaSh

thanks <3

15. campbell_st

then see if the other 2 primes in the teens divides evenly

16. TinaSh

I don't know , I will try to figure it out thanks though

17. freckles

well the key to help was the teenager part

18. TinaSh

yeah , teens

19. freckles

"so they could be 13,17, or 19" exactly two of these numbers will be factors

20. freckles

then you have to find the other factor by divide 7429 by the product of two teenagers

21. freckles

what is 7429 divided by 13 ?

22. TinaSh

2476.3

23. freckles

you should get some kind of remainder that isn't 0 which would mean 13 is not factor of 7429 which means the other two number 17 and 19 are factors of 7429

24. freckles

so you only have to find one last factor

25. freckles

$\frac{7429}{17 \cdot 19}=?$

26. TinaSh

So far I have done , 17/7429 = 437 /23 = 19

27. TinaSh

that leaves me with 1 , if i divide it within 19 itself

28. freckles

is this what you meant to say: $\frac{7429}{17 \cdot 19}=\frac{7429}{323}=23$

29. freckles

which means 17*19*23=7429

30. TinaSh

kinda

31. freckles

oh I think I get what you are saying but those fractions aren't equal

32. freckles

$\frac{7429}{17}=437 \\ \frac{437}{23}=19$

33. freckles

first fraction gives 7429=17(437) then second fraction says 437=23(19)

34. freckles

so replace 437 in 7429=17(437) with 23(19) so 7429=17(23*19)

35. freckles

and you did it girl good job!

36. TinaSh

Oh my gosh thank you so much <3

37. freckles

and 17,19,23 are all prime because they are only divisible by themselves or 1

38. TinaSh

Can I get this straight first XD I wanna be completely sure 17/7421 = 19 divide by 23 or what? Oh my gosh I am confusing myself