Over the past 7 years being a private math tutor I have used various tips and little tricks in helping students. Many students have difficulty finding factors, especially with larger numbers. A tip I give them is that you can first see if the number is even or odd. Any even number is divisible by 2, so I suggest the students start with that to break down the big number in half.

Suppose now the number that you need factors for is 23523. A panic immediately sets in trying to figure out a whole number that divides evenly into that. A trick I use is add the numbers in that, 2+3+5+2+3. That equals 15. If that added number is divisible by 3, then the entire number is as well. Since 15 is divisible by 3 evenly, so is 23523. So two factors of 23523 are 3 and 7841.

I also always tell my students that any number ending in 5 is divisible by 5 and any number ending in 0 is divisible by 5 and 10.

Some tips regarding the sum of the measures of the angles of polygons. What is the measure of the angles of a pentagon? An octagon? A decagon? All anyone really needs to know is the sum of the angles of a triangle and the rest can be obtained easily, as long as you can count the sides and add. The sum of the measures of the angles of a triangle is 180. The square, a 4 sided figure, has angles summing to 360. That is 180 added to the triangle. Same holds true for the pentagon and hexagon and all others. Keep adding 180 for each extra side.

Finding common denominators can be a headache as well. Ideally you would like to find the lowest common denominator to make addition or subtraction easiest and to avoid simplification. But finding any common denominator is the first step in solving a problem. Simplifaction can come later. Take for instance the problem

13/40 + 5/12. The lowest common denominator is 120, but if one cannot see that the easy way to get a common denominator is to multiply the 2 denominators in the problem. Simplification will be needed to finish after addition but it will save headaches trying to find the lowest common denominator if that gives you trouble.

Another very common mistake I see is when squaring an expression. For instance a problem like (x-2)^2 very commonly I see x^2+4 as the answer. The student took x squared and 2 squared and added together. I give the tip to think of something like 2 squared. How do you solve 2 squared? It’s 2 times 2. Multiply the number by itself twice. Same with expressions. The correct multiplication should be x-2 times x-2.

There are other tips, but these are some of the most common problems I see in algebra and geometry and these tips are always helpful!