Question

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?

Answer 1

so we have
\[a \cdot b \cdot c=7429\]

Answer 2

we know prime numbers are odd for the most part

Answer 3

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

Answer 4

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

Answer 5

I would probably try to write the prime factorization of 7429

Answer 6

can you do that?

Answer 7

wait what are prime numbers? :$

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

thanks <3

Answer 15

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

Answer 16

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

Answer 17

well the key to help was the teenager part

Answer 18

yeah , teens

Answer 19

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

Answer 20

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

Answer 21

what is 7429 divided by 13 ?

Answer 22

2476.3

Answer 23

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

Answer 24

so you only have to find one last factor

Answer 25

\[\frac{7429}{17 \cdot 19}=?\]

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

which means 17*19*23=7429

Answer 30

kinda

Answer 31

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

Answer 32

\[\frac{7429}{17}=437 \\ \frac{437}{23}=19\]

Answer 33

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

Answer 34

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

Answer 35

and you did it girl
good job!

Answer 36

Oh my gosh thank you so much <3

Answer 37

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

Answer 38

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