Page 49 - Start Up Mathematics_5

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Factors and Multiples

Let’s Recall ...

• A factor is a smaller number that divides the given number completely
without leaving any remainder. For example, on dividing 86 by 2, the
remainder is 0. So, 2 is a factor of 86. Also, the quotient obtained is 43. So,
43 is also a factor of 86.
• Multiple of a number = The number × Any counting number

For example, the multiples of 9 are 9 × 1 = 9, 9 × 2 = 18, 9 × 3 = 27 and so on.

• Properties of Factors Properties of Multiples
(a) The smallest factor of every (a) Every number is a multiple of
number is 1. itself.

(b) Every number is a factor of (b) A number has unlimited
itself and it is the greatest multiples.
factor of that number. (c) Every number is a multiple
(c) A number can have only a of 1.
limited number of factors. (d) The multiples of a number are

(d) Factors of a number are always either greater than or equal to
smaller than or equal to the the number.
number. (e) Every multiple of a number

is exactly divisible by that
number.

• Numbers are of two types—prime and composite.

Prime Number Composite Number
(a) It has only two factors, 1 and (a) It has more than two factors.
itself.

(b) It cannot be divided exactly by (b) It can be divided exactly by its
any other number other than 1 factors. For example, 4, 6, 8, 9,
and itself. For example, 2, 3, 5, 10, ...
7, 11, ...

• Factorization means writing a number as a product of its factors.

• Prime factorization is writing a composite number as a product of factors that are prime
numbers.

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