Algebra 1 Common Core Student Edition, Grade 8-9

Sk i l l s H a n d b o o k

Pr i m e N u m b er s an d Co m p o si t e N u m b er s

A prim e n u m b e r is a w hole n u m b e r greater th a n 1 th a t h as exactly two factors,
the n u m b e r 1 a n d itself.

Prime num ber 2 5 17 29
Factors 1,2 1,5 1, 17 1,29

A com posite n u m b e r is a n u m b e r th a t h as m ore th a n two factors. The n u m b e r 1 is
neith er prim e n o r com posite.

Composite number 6 1 5 4 8
Factors 1, 2, 3, 6 1, 3, 5, 15 1, 2, 3, 4, 6 , 8 , 12, 16, 24, 48

Ex a m p l e 1

Is 51 prime or com posite?

51 = 3 • 17 Try to find factors other than 1 and 51.

51 is a com posite num ber.

You can use a factor tree to find th e p rim e factors of a num ber. W hen all th e factors
are prim e n um bers, it is called th e p rim e factorization of th e num ber.

Ex a m p l e 2

Use a factor tree to write the prime factorization o f 28.

2 g 28 The order o f listing the factors may be different,

/ \ / \ but the prime factorization is the same.

2 14 4 7

\2 ) [1J [2J (2

The prim e factorization of 28 is 2 • 2 • 7.

Ex e r c i se s

Is each num ber prime or com posite?

1.9 2.16 3.34 4.61 5.7 6.13

7.12 8.40 9.57 10.64 11.120 12.700

List all the factors o f each number.

13.46 14.32 15.11 16.65 17.27 18.29

Use a factor tree to write the prim e factorization o f each number.

19. 18 20. 20 21. 27 22. (^5423). 64 24. 96