Numbers are factors (or divisors) of another number if they multiply to give that number. For example, 3 and 4 are factors of 12 as 3 × 4 = 12.
Algebraic terms x and y are factors of m, if m=xy
For polynomial expressions the same rule applies. For example, x−4 and x−2 are factors of the quadratic expression x2−6x+8 because (x−4)(x−2)=x2−6x+8.
Finger patterns are numbers displayed with fingers on one or two hands. Patterns used to express numbers such as 3 using fingers vary between cultures. Whether 3 is represented by the central 3 fingers on one hand or by 2 fingers on one hand and 1 finger on the other, patterns are formed.
The ‘for each’ idea of multiplication is sometimes used as a way of describing the product of different combinations. For example, if for each sandwich there are two choices of bread and for each choice of bread there are three choices of filling there will be six different sandwich options (2 x 3).
Dividing quantities using fractions as part-whole relationships requires maintaining the multiplicative relationship between each part and the whole. For example, sharing in the ratio 2 parts to 1 part means \(\frac23\) and \(\frac13\) of the whole.