Education.com
Try
Brainzy
Try
Plus

# Tips on Factoring Help (page 2)

based on 1 rating
By — McGraw-Hill Professional
Updated on Sep 27, 2011

#### Example 1:

Factor 1224.

The prime factors to check are 2, 3, 7, 11, 13, 17, 19, 23, 29, 31.

1224 ÷ 2 = 612

612 ÷ 2 = 306

306 ÷ 2 = 153

153 ÷ 3 = 51

51 ÷ 3 = 17

1224 = 2 × 2 × 2 × 3 × 3 × 17

#### Example 2:

Factor 300.

The prime factors to check are 2, 3, 5, 7, 11, 13, 17

300 ÷ 2 = 150

150 ÷ 2 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

300 = 2 × 2 × 3 × 5 × 5

#### Example 3:

Factor 1309.

The prime factors to check are 7, 11, 13, 17, 19, 23, 29, 31

1309 ÷ 7 = 187

187 ÷ 11 = 17

1309 = 7 × 11 × 17

#### Example 4:

Factor 482.

The prime factors to check are 2, 3, 7, 11, 13, 17, 19.

482 ÷ 2 = 241

482 = 2 × 241

Find practice problems and solutions at Tips on Factoring Practice Problems - Set 2.

## Factoring Tips - Prime Factoring Shortcuts

What happens if you need to factor something like 3185? Do you really need all the primes up to 59? Maybe not. Try the smaller primes first. More than likely, one of them will divide the large number. Because 3185 ends in 5, it is divisible by 5: 3185 ÷ 5 = 637. Now all that remains is to find the prime factors of 637, so the list of prime numbers to check stops at 23. The reason this trick works is that a number will not divide 637 unless it also divides 3185. In other words, every divisor of 637 is a divisor of 3185. Once you divide the large number, the list of prime numbers to check will be smaller.

The First Sixteen Prime Numbers

 Prime Number Square of the Prime Number 2 4 3 9 5 25 7 49 11 121 13 169 17 289 19 361 23 529 29 841 31 961 37 1369 41 1681 43 1849 47 2209 53 2809

150 Characters allowed

### Related Questions

#### Q:

See More Questions
Top Worksheet Slideshows