Every integer greater than 1 either is a prime number or a composite number. All composite numbers can be expressed as a product of prime numbers. For example, 6 can be expressed as 2 × 3. The prime factors of 6 are 2 and 3. Whereas the expression 2 × 3 is called prime factorization. Another example, 24 can be expressed as 2 × 2 × 2 × 3. The prime factors of 24 are 2 and 3. Whereas the expression 2 × 2 × 2 × 3 is called prime factorization. Similarly, 45 = (3)(3)(5). The prime factors of 45...

Let's see how we use the chart to deal with this question: How many positive factors does 100 have? Set up the chart: 100 Left Column Right Column 1 100 2 50 4 25 5 20 10 10   Remember the rule - once the factors repeat themselves, (i.e. 10 and 10), stop. Since 10 cannot be counted twice as a factor, you're left with 9 factors: 1, 2, 4, 5, 10, 20, 25, 50, 100. What we have here is a special case of finding the number of factors for a perfect square - an integer whose square root is also...

You've already seen the wonderful factor table - a simple technique for finding all the factors of an integer. Let's see how we use the chart to deal with this question: How many positive factors does 140 have? The question asks about factors, so the factor table is appropriate. Set up the table: 140 Left Column Right Column 1 140 2 70 4 .....             And let's pause for a second. Because 140/4 is the first calculation that requires a bit of work. Which brings...

Some integer questions may require you to find the Factors of an integer. The factor table is a basic technique for finding all the factors of any integer. This technique can also be useful for questions asking how many factors a particular integer has. The technique goes as follows: Write the original integer on top of the table. Divide the original Integer by the smallest positive factor: 1. Write "1" in the left column, and the result of the division in the right column. (Of course, this...

Primes play a central part in integer questions. Overconfidence is dangerous here: while almost everybody can recite the definition of a prime number at the drop of a hat, the field is actually rife with misconceptions. We are here to make sure you know everything there is to know about primes. To understand primes, let's first take a look at the definition of a prime: "A prime number is a positive integer with exactly two distinct positive factors: 1 and itself". 5 is a prime number because...

Let's formulate rules for addition, subtraction, multiplication, and division of Even and Odd numbers. Here are the rules for adding / subtracting even and odd numbers: Even ± Even = Even (e.g. 2 + 2 = 4; -4 - 2 = -6) Odd ± Odd = Even (e.g. 1 + 1 = 2; -31 - 1 = -32) Even ± Odd = Odd (e.g. 2 + 1 = 3; -12 - 1 = -13) There are some very important observations here. If you add or subtract any quantity of even numbers, the result will always be even. For example, -2 + 8 + 20 - 16 = 10 (even) -2 + 8...

We'll begin with the basic definitions: Even: any integer that is divisible by 2. Examples: 2, 4, 14. Odd: any integer that is not divisible by 2, i.e. leaves a remainder of 1 when divided by 2. Examples: 1, 3, 5, 7, 9 So far so good. Consider this potential misconception: Is 0 even or odd? When dividing 0 by 2, you get a result of 0 ÷ 2 = 0. In other words, 0 is divisible by 2. Therefore, zero meets the criteria set for even integers. Hence zero is even. Zero is neutral when it comes to...