# Generalizing the Problem

Generalizing is making broad statements about a solution, and realizing that the solution to one problem may apply to many other problems.

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Here is a simply problem to demonstrate generalization:

Let us investigate the divisibility by 2 (test of divisibility by 2).

 Remainder Exactly divisible or not 420 ÷ 2 0 Divisible 321 ÷ 2 1 Not Divisible 8922 ÷ 2 0 Divisible 2423 ÷ 2 1 Not Divisible 124 ÷ 2 0 Divisible 25 ÷ 2 1 Not Divisible 326 ÷ 2 0 Divisible 427 ÷ 2 1 Not Divisible 28 ÷ 2 0 Divisible 629 ÷ 2 1 Not Divisible

After observing the division facts on the above table, we may generalize that:

• the numbers ending in 0, 2, 4, 6, 8 are divisible by 2
• the numbers ending in 1, 3, 5, 7, 9 are not divisible by 2

Further, we may generalize that all even numbers are divisible by 2, and that all odd numbers are not divisible by 2.

This generalization is now useful in answering question such as, "Is 45974 divisible by 2?"

We don't need to do any math. We can state the answer is "yes," since 45974 an even number.

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