MULTIPLES AND FACTORS
What are factors?
Factors are the numbers that can divide a number exactly. Hence, after division, there is no remainder left. Factors are the numbers you multiply together to get another number. Thus, a factor is the divisor of another number
Ex :a = 3, b =45, then a divides b
a is a factor of b
What are multiples ?
A multiple is a result obtained by multiplying a number by an integer (it shouldn’t be a fraction). The multiples of the whole number are obtained by taking out the product of the counting numbers and that of whole numbers
Ex : 6, 12, 18, ....... are multiples of 6.
Factors of 6 are 1, 2, 3, 6
Note 1 : Every number is muliple of itself and also factor of itself.
2. For every number there are infinite multiples.
Ex :\(5(5 \times 1),\,\,\,10(5 \times 2),\,\,15(5 \times 3)\) ,......
Number of factors of a number are finite.
Ex : 125 = 125 x 1
125 = 5 x 5 x 5
The number of factors of 125 are 3. (1,5,125).
Key Points:
Every whole number has an infinite number of multiples.
The multiples of a number form a sequence.
Zero is a multiple of every number, as 0×n=0 for any number n.
Negative numbers can also be multiples, obtained by multiplying a negative integer by a positive number