how do you do for factors and divisibility
To find factors and test for divisibility, you can follow these steps:
1. Factors: Factors are the numbers that evenly divide into a given number. To find the factors of a number, you need to divide it by all numbers from 1 up to the square root of the number, and if the division is exact (i.e., it leaves no remainder), then those numbers are factors.
For example, to find the factors of 12:
- Divide 12 by 1: 12 ÷ 1 = 12 (no remainder)
- Divide 12 by 2: 12 ÷ 2 = 6 (no remainder)
- Divide 12 by 3: 12 ÷ 3 = 4 (no remainder)
- Divide 12 by 4: 12 ÷ 4 = 3 (no remainder)
So, the factors of 12 are 1, 2, 3, 4, 6, and 12.
2. Divisibility: Divisibility refers to whether a number can be divided evenly by another number without leaving a remainder. Here are some rules for testing divisibility by certain numbers:
- Divisible by 2: If the last digit of a number is even (ends in 0, 2, 4, 6, or 8), then it is divisible by 2. For example, 36 is divisible by 2 because its last digit is 6.
- Divisible by 3: If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3. For example, 123 is divisible by 3 because 1 + 2 + 3 = 6, which is divisible by 3.
- Divisible by 4: If the last two digits of a number form a number divisible by 4, then the number itself is divisible by 4. For example, 512 is divisible by 4 because 12 (last two digits) is divisible by 4.
- Divisible by 5: If the last digit of a number is 0 or 5, then it is divisible by 5. For example, 75 is divisible by 5 because its last digit is 5.
- Divisible by 6: If a number is divisible by both 2 and 3, then it is divisible by 6. For example, 60 is divisible by 2 and 3.
- Divisible by 9: If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9. For example, 315 is divisible by 9 because 3 + 1 + 5 = 9, which is divisible by 9.
- Divisible by 10: If a number ends with a 0, then it is divisible by 10. For example, 100 is divisible by 10.
By following these rules, you can determine if a given number is divisible by another or find its factors.