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~=M-l&10._ ~=M•l&10._
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6 rn
12 8
16~1~4
48
a 24---- --a Open: design sorting diagrams to
4' ~ \ 2 show the common factors (highest
common factor to be ringed) of
b (1,48), (2,24), (3, 16), (4, 12), (6,8), these pairs of numbers:
(8,6), (12,4), (16,3), (24,4), {48, 1)
a

Factors Factors
5
a Open: draw ray diagrams for six of 12 of 20
numbers between 20 and 50 and
list their factor pairs. b
21
Possible solutions:
Factors Factors
37: ( 1 ,37) (37' 1)
25: ( 1 ,25) (5,5) (25, 1) of 28 4 of 42
46: ( 1 ,46) (2,23) (23,2) (46, 1)
28: {1,28) {2,14) (4,7) (7,4) {14,2) {28,1) c
40: {1,40) (2,20) (4, 10) (5,8) (8,5) {10,4) (20,2) (40, 1)
36: ( 1 ,36) (2, 18) (3, 12) (4, q) {6,6) {q ,4) ( 12,3) ( 18,2) (36, 1) a If you divide one number by another and the answer Factors Factors
has no remainder on the calculator, both the divisor
b The factors of every number include 1 and the of 15 7 of 35
and the answer are factors of the original number.
number itself. The number of factors of each
number is even (with the exception of square b Open: design a different diagram to show the d 24
numbers). common factors (and highest common factor) of 65
and q1.
Factors Factors
Challenge set of factors for 65 = {1,5, 13,65} of 24 8 of 36
set of factors for q1 = {1,7, 13,q1}
Practical: copy and complete a database for 1 and 13 are common factors of 20 and 12
numbers up to 25. 13 is the highest common factor of 20 and 12 e 45
Five numbers with odd numbers of factors: 5
1, 4, q, 16, 25. Challenge Factors Factors
The numbers with odd number of factors are all The completed diagram should give the following sets: of 27 of 45
square numbers. Factors of 35 {1, 5, 7, 35}
Four other numbers less than 100 with odd number of Factors of 63 {1, 3, 7, q, 21, 63} f
63
factors: 36, 4q, 64, 81. Factors of 54 {1, 2, 3, 6, q, 18, 27, 54}
Factors Factors
of 42 q of 63