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Tips on Factoring Help (page 2)

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

Examples

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

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