Question

Write the number of factors of the following?
90

Answer 1

Hint:The Factors of 90 are all the integers (positive and negative whole numbers) that you can evenly divide into 90. 90 divided by a Factor of 90 will equal another Factor of 90.
It is a two-step process to create all the Factor Pairs of 90: First, we list all the factors of 90. Then, we pair all the different combinations of factors to give you all the Factor Pairs of 90.

Complete step-by-step answer:
Since the Factors of 90 are all the numbers that you can evenly divide into 90, we simply need to divide 90 by all numbers up to 90 to see which ones result in an even quotient. When we did that, we found that these calculations resulted in an even quotient:
90 ÷ 1 = 90
90 ÷ 2 = 45
90 ÷ 3 = 30
90 ÷ 5 = 18
90 ÷ 6 = 15
90 ÷ 9 = 10
90 ÷ 10 = 9
90 ÷ 15 = 6
90 ÷ 18 = 5
90 ÷ 30 = 3
90 ÷ 45 = 2
90 ÷ 90 = 1
The Positive Factors of 90 are therefore all the numbers we used to divide (divisors) above to get an even number.
All the different pair combinations from the factors of 90 above are the Factor Pairs of 90. Below is the list of all the Factor Pairs of 90. As you can see, all Factor Pairs of 90 equal 90 when you multiply them together.
\[\begin{array}{*{20}{l}}
  {1{\text{ }}{\rm X}{\text{ }}90{\text{ }} = {\text{ }}90} \\
  {2{\text{ }}{\rm X}{\text{ }}45{\text{ }} = {\text{ }}90} \\
  {3{\text{ }}{\rm X}{\text{ }}30{\text{ }} = {\text{ }}90} \\
  {5{\text{ }}{\rm X}{\text{ }}18{\text{ }} = {\text{ }}90} \\
  {6{\text{ }}{\rm X}{\text{ }}15{\text{ }} = {\text{ }}90} \\
  {9{\text{ }}{\rm X}{\text{ }}10{\text{ }} = {\text{ }}90} \\
  {10{\text{ }}{\rm X}{\text{ }}9{\text{ }} = {\text{ }}90} \\
  {15{\text{ }}{\rm X}{\text{ }}6{\text{ }} = {\text{ }}90} \\
  {18{\text{ }}{\rm X}{\text{ }}5{\text{ }} = {\text{ }}90} \\
  {30{\text{ }}{\rm X}{\text{ }}3{\text{ }} = {\text{ }}90} \\
  {45{\text{ }}{\rm X}{\text{ }}2{\text{ }} = {\text{ }}90} \\
  {90{\text{ }}{\rm X}{\text{ }}1{\text{ }} = {\text{ }}90}
\end{array}\]
Here is the list of all Positive Factors of 90 in numerical order:
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

Note:Factors are whole numbers or integers that are multiplied together to produce a given number. The integers or whole numbers multiplied are factors of the given number. If x multiplied by y = z then x and y are factors of z. Factors is like division in maths, because it gives all numbers that divide evenly into a number with no remainder. An example is number 8. it is evenly divisible by 2 and 4, which means that both 2 and 4 are factors of number 8.