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Multiplying Multiples of Numbers Together

To multiply multiples of numbers togethers, it is sometimes easier to use the square of the base number and the factor within the other number.

 

Example:

13 × 26 =

Solution:

Notice that 26 is a multiple of 13 and, in fact, 26 = 2(13). Therefore, 13 × 26 = 13 × (13 × 2) = 13 2 × 2.

Knowing that 13 2 = 169, you can easily multiply 169 × 2 = 338.

Answer:

13 × 26 = 338.

 

Example:

34 × 51 =

Solution:

This problem is a little different from the first since 51 is not a multiple of 34. However, both 34 and 51 are multiples of 17. Therefore, 34 × 51 = (17 × 2) × (17 × 3) = 17 2 × 2 × 3 = 17 2 × 6. Multiplying this out, we get 289 × 6 = 1734.

Answer:

34 × 51 = 1734.

 
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