The prime factorization of a number is when you break it down into the very basic prime numbers that, when multiplied together, will equal that final number.
Right off the bat, we can see that 1260 is an even number, so we will start by dividing by 2, since all even numbers are divisible by 2
1260 / 2 = 630
Again, the number is obviously divisible by 2, so we will do it again
630 / 2 = 315
315 is not divisible by 2, so let us check if it is divisible by 3.
A proven way to do this is to add the individual numbers in the bigger number, and if that number is divisible by 3, then the bigger number is also divisible by 3.
3 + 1 + 5 = 9
9 is divisible by 3, so we know that 315 is also divisible by 3.
315 / 3 = 105
If any number (except 0) ends with a 5 or a 0, then it is divisible by 5.
105 / 5 = 21
21 is again divisible by 3
21 / 3 = 7
So there are our prime factor numbers.
The prime factorization of 1260 is as follows:
2 * 2 * 3 * 3 * 5 * 7
Hope that helped =)