Multiples and Factors

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Factors and Multiples

Factors and multiples are key concepts in arithmetic and number theory. Understanding these helps in simplifying numbers and solving a variety of math problems.

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FACTORS

A factor of a number is any whole number that divides the original number exactly, without leaving a remainder. In other words, if a number can be multiplied by another number to give the original number, those two numbers are factors of the original number.

For example:

The factors of 12 are 1, 2, 3, 4, 6, and 12 because:
1 x 12 = 12
2 × 6 = 12
3 × 4 = 12

MULTIPLES

A multiple of a number is the result of multiplying that number by any whole number. Multiples continue infinitely and grow larger as you multiply by bigger numbers.

For example:

The multiples of 5 are 5, 10, 15, 20, 25, ... and so on, because:
5 x 1 = 5
5 × 2 = 10
5 × 3 = 15

... and this continues.

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Key Differences:

Factors are smaller or equal to the number, and they divide it exactly.

Multiples are larger or equal to the number, formed by multiplying it.

For example:

The factors of 6 are 1, 2, 3, and 6.

The multiples of 6 are 6, 12, 18, 24, ... and so on.

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Real-Life Example:

If you're arranging objects in rows, factors help you figure out how many items can go in each row without leaving any leftovers. Multiples can tell you the total number of objects you’ll have if you multiply them in groups.

Understanding factors and multiples is important for simplifying fractions, solving problems in algebra, and finding common denominators in arithmetic.

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