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To test whether a fraction is in lowest terms, you need to know the divisors of both the numerator and the denominator. There are some tricks that will help you know if one number is divisible by another. 2—Even numbers are divisible by 2, odd numbers are not. Ex. 34761982832 is divisible by 2 since it is even 3—A number is divisible by 3 when the sum of the digits is divisible by 3. Ex. 78 is divisible by 3 because 7+8=15 which is divisible by 3. Ex. 54387924 is divisible by 3 because 5+4+3+8+7+9+2+4=42 and 4+6 which is divisible by 3. 4—A number is divisible by 4 when the last 2 digits are divisible by 4. Ex. 89765463828 is divisible by 4 because 28 is divisible by 4. 5—A number is divisible by 5 if the last digit is a 5 or a 0. Ex. 23659874125 is divisible by 5. 6—A number is divisible by 6 if it is divisible by both 2 and 3. Ex. 78 is divisible by both 2 and 3 so it is divisible by 6. 7—There are tricks but they are complicated and it is usually easier to just divide by 7 and see if it works. 8—A number is divisible by 8 if the last 3 digits are divisible by 8. Ex. This is useful when working with large numbers. Ex. To see if 987463120 is divisible by 8 we only need to check if 120 is divisible by 8. It is so 987463120 is divisible by 8 9—A number is divisible by 9 when the sum of the digits is divisible by 9. Ex. To check if 213654951 is divisible by 9 add. 2+1+3+6+5+4+9+5+1=36. 36 is divisible by 9 so 213654951 is divisible by 9. 10—A number is divisible by 10 if the last digit is 0. 11—A number is divisible by 11 if the alternating sum of the digits is divisible by 11. Ex. To check if 65432532 is divisible by 11 look at 6-5+4-3+2-5+3-2=0. Since 0 is divisible by 11 (11 goes into 0 zero times) 65432532 is divisible by 0 also. You can stop when you get to the square root of a number—2 numbers that multiply to make your number have to have 1 above the square root and one below the square root so once you get to the square root you should have gotten one. Ex. The square root of 225 is 15. I can write 225 as a 1 225 3 75 multiplication like this 5 45 . Every equation has one number that is less than or equal to the square 9 25 15 15 root and one that is greater than or equal to the square root. If your number is not divisible by anything less than the square root that the number is prime and has no factors. Ex. Simplify 102 306 102 and 306 are both divisible by 2 102 306 2 51 2 153 51 153 Now let’s check if either is divisible by 3. For 51 we take 5+1=6 which is divisible by 3 so 51 is divisible by 3. For 153 we take 1+5=3=9 which is divisible by 3 so both are divisible by 3. 51 153 3 17 17 3 51 51 We already know that 51 is divisible by 3 so we get 17 51 17 3 17 1 3 If we needed to find a number that goes into 17, we would only have to check if it is divisible by 2, 3 or 4 because the square root of 17 is just over 4. It turns out that 17 is prime.