# Notes on Factors…Part 1(Factor,Multiples)

Any number that can divide another number EXACTLY is called its  factor or

A factor of a number is an exact divisor of that number.

Smallest factor of a number is 1 and largest factor is number itself.

There may be other factors in between smallest and largest factors that can divide the given number exactly without leaving any remainder.

For example, for number 20, factors are 1, 2, 4, 5, 10, 20.  One important fact is that number 20 is a multiple of all of its factors e.g.

1×20=20,  2×10=20,  4×5=20,  5×4=20,  10×2=20,  20×1=20.

Similarly, factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

Any two numbers when multiplied together produce third number that is called the product of two numbers e.g.4×6=24. This number 24 is also called the multiple of 4 and 6. Multiplying numbers 4 and 6 are called factors of 24. Similarly pair of all such numbers that give a product of 24, are the factors of 24. Such possible pair of numbers are 1,24; 2,12; 3,8; 4,6; 6,4; 8,3; 12,2 and 24,1. Therefore numbers 1, 2, 3, 4, 6, 8, 12, 24 are factors of 24(repetition of numbers is ignored while listing the factors)

Multiples

When a given number 24 is multiplied by numbers 1, 2, 3, 4, 5, 6……, their product is 24, 48, 72, 96, 120,144……… and these are called the multiples of 24. There may be thousands and thousands of multiplying

numbers to 24 and they produce infinite multiples of 24. Lowest multiple of any number is number itself.

From above following facts are noticed-

1.  1 is a factor of every number.

2.  every number is a factor of itself.

3.  every factor of a number is an exact divisor of that number.

4.  every factor is less than or equal to the given number.

5.  number of factors of a given number are finite.

6.  every multiple of a number is greater than or equal to that number.

7.  the number of multiples of a given number is infinite.

8.  every number is a multiple of itself.

Updated: June 5, 2014 — 3:10 am
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