Arithmetic/More About Multiplication

Factors and MultiplesEdit

Is One a Factor of Everything?Edit

To answer the question above, yes. 1 is a factor of any number n. For proof, consider this statement: "any number n is a factor of itself when multiplied by one".

 
let n = any number, then any number times 1 is itself. This picture also demonstrates the commutative property of multiplication which basically means the operation of multiplication can be performed in any order.

Proof: Let n = 27 then 27 * 1 = 27 because any number multiplied by 1 is itself. The reason for this is say you had a bag of 12 marbles. If you had 2 bags of marbles you would have 24 marbles because 12 is multiplied by the number 2 because you have 2 bags. However, if you only have 1 bag of 12 marbles, you only have 12 marbles. Therefore, we know this statement to be a fact: Any number n can be factored to n * 1.

58 million times 1? Answer: 58 million. It does not matter how big the number(or even how small, as in this example: 1*(-245) = -245.) Though, negative numbers are beyond the scope of this page, as you continue to increase your understanding of mathematics, you will learn of negative numbers and absolute value.

Is Zero a Factor of Anything?Edit

To answer the question above, no.

A number is a factor of another number if it can be multiplied by a whole number to give the number is it a factor of. Anything multiplied by zero is also zero, which means that the only number that could possibly have zero as a factor is zero itself.

Phrased differently, the multiples of 0 go 0, 0, 0, 0... and so on, never becoming any larger than 0. Since a factor is the reverse of a multiple, there are no numbers other than 0 with a factor of 0 as well.

A Look Ahead at Prime NumbersEdit

The Greatest Common FactorEdit

The Greatest common Factor (GCF) of two whole numbers is the highest number that can be divided by both of the original numbers to get a whole number result.

Finding the GCF of a numberEdit

  1. Write down to prime factorization of the two numbers.
  2. Find prime factors that are the same.
  3. Multiply the same prime factors together for the GCF.

ExampleEdit

  1.  
     
  2. Notice that two and seven are used in both the equations?
  3.  
    Therefore, the GCF of 28 and 98 is 14.

The Least Common MultipleEdit