All numbers are divisible by one. Because of this, one is often excluded from a list of factors unless it is one of only two numbers. For instance, the factors of seven would be listed as one and seven, but the factors of eight would only include two, four and eight.
Two is a factor of all even numbers. To determine whether a number is even or odd, look at the last digit. If it is zero, two, four, six or eight, the number is even, and two is a factor of that number. For instance, even though 1,946 is a large number, you can know by looking at it that two is a factor, because the last digit is six, making it an even number.
To determine whether three is a factor of a number, first add the number's digits. If the sum of the digits is divisible by three, then three is a factor of that number. For example, three is a factor of 711 because the sum of its digits is nine, and nine is divisible by three. Three is not a factor of 712, however, because the sum of the numbers, 10, which is not divisible by three.
Four is a factor of a number if it is a factor of the number formed by its last two digits. Do not add the digits, but rather look at the number that they make when placed side by side. For example, in the number 182,812, the last two digits make the number 12. 12 is divisible by four, therefore four is a factor of 182,812.
Five is a factor of all numbers that end in zero or five. To remember this rule, simply count by fives and notice the pattern: 5 10, 15, 20, 25, 30 and so on. All of these numbers end with zero or five, a pattern which holds true for all numbers with a factor of five.
Six is a factor of a number if both two and three are also factors. For example, 12 is divisible by two because the last number is even. Three is also a factor, because the sum of the numbers equals three. Since it is divisible by both two and three, it is also divisible by six.
To determine whether seven is a factor of a number, double the last digit of the number, then subtract the result from the remaining number. If the answer is zero or is divisible by seven, then seven is a factor of that number. For instance, the last digit of 126 is six, which when doubled, equals 12. The remaining number is also 12, and 12 minus 12 equals zero. Therefore, seven is a factor of 126.
If the last three digits of a number are divisible by eight, eight is a factor of that number. For example, eight is a factor of 13,120 because 120 is divisible by eight. 13,125 is not divisible by eight because eight is not a factor of 125.
Nine is a factor of a number if the sum of the digits is divisible by nine. For example, nine is a factor of 1,881 because the sum of its digits equals 18. Nine is a factor of 18, therefore it is also a factor of 1,881.
Ten is a factor of any number ending in zero. As with five, to remember this rule, simply count by tens and note the pattern in the numbers. 10, 20, 30, 40, 50, etc., all end in zero, as do all other numbers that can be factored by 10.