Question

How are factors and products related?

Answer 1

Hint: From the question we have to explain the relation between factors and products. Factor means multiplying two numbers gives a product. The numbers that we multiply are the factors of the product. Product means the result of two numbers when multiplied together.

Complete step-by-step answer:
We know that,
Factor means multiplying two numbers gives a product. The numbers that we multiply are the factors of the product.
Product means the result of two numbers when multiplied together.
For example:
\[\Rightarrow \dfrac{30}{6}=5\]
 and there is no remainder.
 So, we can say that \[5\] and \[6\] are the factors of \[30\].
In the given example, we can further break up or simplify the number \[6\] into its factors, that is, \[2\]and \[3\] . In other words, when we multiply \[5,\text{ }2\text{ and }3\], we still get \[30\]. Therefore, the factors of \[30\] are \[5,\text{ }2\text{ and }3\]. Also, \[\text{5}\times 2\text{ }=\text{ }10\]. So, \[10\] is also a factor of \[30\]. Similarly, \[5\times 3\text{ }=\text{ }15\]. So, \[15\] is also a factor of \[30\]. Finally, the factors of \[30\] are \[1,\text{ }2,\text{ }3,\text{ }5,\text{ }6,\text{ }10,\text{ }15\text{ }and\text{ }30\].
And the product is \[30\].

Note: Students should know the relation between the factor and product. Student should also remember some points like, the number \[1\] is the smallest factor of every number. Every number will have a minimum of two factors, \[1\] and the number itself. A number that has only two factors, \[1\] and the number itself, is called a prime number. Factors are always whole numbers or integers and never be decimal or fractions. All even numbers will have number \[2\] as their factor. All numbers that end with \[5\] will have \[5\] as their factor. All numbers greater than o and ending with a o will have \[2\],\[5\], and \[10\] as their factors. Algebraic expressions are often solved or simplified through factoring.