Remainders
Remainder divided by 3
Find the sum of all the digits of the number and find the remainder of that number divided by 3. For Example: What is the remainder of 12009843092 / 3 (1 + 2 + 0 + 0 + 9 + 8 + 4 + 3 + 0 + 9 + 2) / 3 = 38 / 3 has remainder of 2 So the answer is 2
Remainder divided by 2
If the number is even, the remainder is 0. If the number is odd, the remainder is 1. For Example: 93274092830948 / 2 has a remainder of what? 93274092830948 is an even number so the remainder is 0 The answer is 0
Remainder of x^n / m
Just say we had 59^7 / 7. There is no trick for dividing by 7 so this question is pretty common on the number sense test. You have to break up 59^7 into 59 × 59 × 59 × 59 × 59 × 59 × 59 which is now an expression. We know now that 59 / 7 has a remainder of 3. Now we have 3 ^ 7 or 3 × 3 × 3 × 3 × 3 × 3 × 3. We can combine three of the pairs of 3's Now it is (3 × 3) × (3 × 3) × (3 × 3) × 3 or 9 × 9 × 9 × 3. The remainder of all the nines divided by 7 is 2 so now we have 2 × 2 × 2 × 3, 8 × 3, 24 / 7 has a remainder of 3. The answer is 3.
Remainder of expressions
When finding the remainder of expression, you can find the remainder of each individual term. Example: [47 + 79 × 6969 - 10 × 5369]/3 has a remainder of what? 47 / 3 has a remainder of 2 79 / 3 has a remainder of 1 6969 / 3 has a remainder of 0 10 / 3 has a remainder of 1 5369 / 3 has a remainder of 2 now we have: [2 + 1 × 0 - 1 × 2]/3 which has a remainder of 0. The answer is 0.
Remainder divided by 11
Find the sum of the alternating digits (starting at the leftmost digit) then find the sum of the remaining digits and subtract them. For Example: 9021849 / 11 The sum of the alternating digits: 9 + 2 + 8 + 9 = 28 The sum of the remaining digits: 0 + 1 + 4 = 5 28 - 5 = 23, since 23 is greater than 11, we have to find the remainder of 23 / 11 which is 1 The answer is 1
Remainder divided by 4
Find the remainder of the first 2 digits divided by 4. For Example: What is the remainder of 12345 / 4 ? The first 2 digits are 45: 45 / 4 has a remainder of 1 The answer is 1
Remainder divided by 8
Find the remainder of the first 3 digits divided by 8 For Example: 4890852 / 8 has a remainder of what? 852 are the last 3 digits: 852 / 8 has a remainder of 4. The answer is 4
Remainder divided by 9
Find the sum of all the digits of the number and find the remainder of that number divided by 9. For Example: 93076 / 9 has a Remainder of what? (9 + 3 + 0 + 7 + 6) / 9 = 25 / 9 which has a remainder of 7 The answer is 7.
Remainder divided by 6
First find the remainder when the number is divided by 2(we will call this remainder #1). Then find the remainder when the number is divided by 3 (we will call this remainder #2). We need to find a number (1 - 6) that has remainder of #1 when it is divided by 2 and a remainder of #2 when divided by 3. For Example: 6969123 / 6 has a Remainder of what? Remainder divided by 2: number is odd so the remainder is 1. Remainder divided by 3: (6+9+6+9+1+2+3)/3 = 36/3. This remainder is 0. The number (1 - 6) that has a remainder of 1 when divided by 2 and a remainder of 0 when divided by 3 is 3 so the remainder of 6969123/6 is 3 The answer is 3
Remainder divided by 5
If the units digit of the number is less than 5, then the remainder is the units digit. If the units digit is 5 or 0, then the remainder is 0. If the units digit is greater than 5, then the remainder is the units digit minus 5. For Example: 39489 / 5 The units digit is 9. Since it is greater than 5, you will do 9 - 5 = 4. The answer is 4
