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Factors and Divisibility Copy the following numbers and chart into your notebook. 22 120 333 52 135 999 Test Number 22 52 122 152 156 222 252 256 20 7984 120 135 530 730 820 835 984 321 35 1984 333 999 122 530 0 152 730 1 156 820 2 222 835 3 252 984 256 321 Divisor 4 5 6 20 35 7 7984 1984 8 9 10 Activity: For each of the following numbers, determine the divisibility rule (or Pattern that tells you if a number can be divided by it) 0 1 2 3 4 5 6 7 8 9 10 Divisible Rules 0 No number is divisible by 0. If a number is divided by 0, it is called undefined (you will learn more about this in high school) 1 All numbers are divisible by 1. All numbers are actually understood to be over 1, but we just do not write it. 2 All even numbers are divisible by 2. If the number ends in 0, 2, 4, 6, or 8, then it is divisible by 2 3 If the sum of the digits (digital root) of the number is divisible by 3, then the entire number is divisible by 3. For example, 7392 = 7 + 3 + 9 + 2 = 21. Since 21 is divisible by 3, then 7392 is divisible by 3. 4 If the last two digits are divisible by 4 then the entire number is divisible by 4. For example, 8316. Since the last 2 digits are 16 and 16 is divisible by 4, then 8316 is divisible by 4. 5 All numbers that end in a 0 or a 5 are divisible by 5. 6 If a number is divisible by 3 and is an even number (which means that it is divisible by 2), then it is divisible by 6. 7 There is NO rule for determining if a number is divisible by 7. 8 If the last 3 digits of a number is divisible by 8, then the number is divisible by 8. For example, 23,848. Since the last 3 digits of 848 is divisible by 8, then 23,848 is divisible by 8 9 If the sum of the digits (digital root) of the number is divisible by 9, then the entire number is divisible by 9. For example, 76,347 = 7 + 6 + 3 + 4 + 7 = 27. Since 27 is divisible by 9, then 76, 347 is also divisible by 9. All numbers that end in a 0 are divisible by 10. 10 Digital Root: when you add up all of the individual digits of a number and you continue doing this until you end up with a single digit number. For Example: 76,233 7+6+2+3+3 = 21 =2+1 =3 Therefore, the digital root of 76,233 is 3. This also means that 76, 233 is divisible by 3. Prime Number: a number that only has two factors, 1 and itself. For Example: 7 23 The factors of 7 are 1 and 7 The factors of 23 are 1 and 23