How to Calculate Divisibility By Single Digit Numbers

Step-by-Step Guide

1. 1

   Step 1: Divide any number by 1.

   Every number has 1 as a factor.This is because any number (x{\displaystyle x}), is equal to 1×x{\displaystyle 1\times x}.
   
   For example, 168,293 is divisible by 1, since 1×168,293=168,293{\displaystyle 1\times 168,293=168,293}.
2. 2

   Step 2: Divide even numbers by 2.

   By definition, an even number is one that is divisible by
   2..
   
   So to check if any number, no matter how long, is divisible by 2, look at the last digit.
   
   If the last digit is even, the entire number is divisible by
   2.Remember that 0 is an even number., To do this, add up all the digits in the number.
   
   If the sum of all digits is divisible by 3, the number is divisible by
   3.You can repeat the addition of digits if the original sum is too long for you to gauge divisibility by
   3.For example, the digits in 3,989,978,579,968,769,877 add up to
   141.
   
   You can then add again: 1+4+1=6{\displaystyle 1+4+1=6}.
   
   Since 6 is divisible by 3, you know the entire number is divisible by
   3. , Look at the last two digits in the number.
   
   Is the number made by the last two digits divisible by 4? If so, the entire number is divisible by
   4.Note that only even numbers are divisible by
   4.
   
   Multiples of 100 are always divisible by
   4.Another way to check for divisibility by 4 is to divide the number by 2 twice.
   
   If the quotient is still a whole number, the original number is divisible by
   4.For example, 8762=438{\displaystyle {\frac {876}{2}}=438}, and then 4382=219{\displaystyle {\frac {438}{2}}=219}.
   
   Since 219 is a whole number, you know that 876 is divisible by
   4. , Since any number ending in 0 or 5 is a multiple of 5, any number whose last digit is 0 or 5 is divisible by
   5., If a number is even, and the sum of its digits are divisible by 3, then the number is divisible by
   6.
   
   In other words, if a number is divisible by 2 and 3, it is divisible by
   6., Separate the last digit from the rest of the number.
   
   Double the last digit.
   
   Then, subtract that product from the number made by the remaining digits.
   
   If the difference is divisible by 7, then the whole number is divisible by
   7.For example, to find out if 567 is divisible by 7, first separate the last digit from the number.
   
   This gives you 56 and
   7.
   
   Double the last digit, 7: 7×2=14{\displaystyle 7\times 2=14}.
   
   Then, subtract 14 from 56: 56−14=42{\displaystyle 56-14=42}.
   
   Since 42 is divisible by 7, you know that 567 is divisible by
   7. , Look at the last three digits in the number.
   
   If the number they make is divisible by 8, then the entire number is divisible by
   8.Another way to do this is to halve the last three digits 3 times.
   
   If the final quotient is a whole number, then the entire number is divisible by
   8.For example, 1282=64{\displaystyle {\frac {128}{2}}=64}, then 642=32{\displaystyle {\frac {64}{2}}=32}, then 322=16{\displaystyle {\frac {32}{2}}=16}.
   
   Since 16 is a whole number, you know that the number 11,128 is divisible by
   8. , A number is divisible by 9 if the sum of its digits is divisible by
   9..
   
   You can repeat the addition of digits if the original sum is too long for you to gauge divisibility by
   9.For example, the digits in 3,989,978,579,968,769,877 add up to
   141.
   
   You can then add again: 1+4+1=6{\displaystyle 1+4+1=6}.
   
   Since 6 is not divisible by 9, you know the entire number is not divisible by
   9. , The test for determining whether a number is divisible by 6 is twofold.
   
   First determine whether the number is even. 456 is even, since it ends in
   6.
   
   Then, determine whether the sum of the digits is divisible by
   3.
   
   So, you would calculate 4+5+6=15{\displaystyle 4+5+6=15}.
   
   The number 15 is divisible by
   3.
   
   Since 456 passes both tests, it is divisible by
   6. , Which digits will evenly divide into this number? 1 divides evenly into the number, since any number is divisible by
   1. 2 divides evenly into the number, since 1,336 is even. 3 does not divide evenly into the number, since the sum of its digits is 13, and 13 is not divisible by
   3. 4 divides evenly into the number, since the last two digits, 36, is divisible by
   4. 5 does not divide evenly into the number, since 1,336 does not end in 5 or
   0. 6 does not divide evenly into the number.
   
   While it is an even number, the sum of its digits is not divisible by
   3. 7 does not divide evenly into the number.
   
   When you double the last digit (6), and subtract it from the remaining digits, you get 133−12=121{\displaystyle 133-12=121}.
   
   Since 121 is not divisible by 7, neither is 1,336. 8 divides evenly into the number, since the last three digits, 336, is divisible by
   8. 9 does not divide evenly into the number, since the sum of its digits is 13, and 13 is not divisible by
   9. , Brian is a kindergarten teacher.
   
   He has 363 crayons.
   
   He divides his class into four groups.
   
   Can he evenly divide the crayons among the four groups? He cannot evenly divide the crayons among the four groups. 363 is not divisible by 4, since it is not an even number, and since the number made from the last two digits, 63, is not divisible by
   4.
3. 3

   Step 3: Check for divisibility by 3.

4. 4

   Step 4: Check for divisibility by 4.

5. 5

   Step 5: Divide numbers ending in 0 or 5 by 5.

6. 6

   Step 6: Check for divisibility by 6.

7. 7

   Step 7: Check for divisibility by 7.

8. 8

   Step 8: Check for divisibility by 8.

9. 9

   Step 9: Check for divisibility by 9.

10. 10

    Step 10: Determine whether the number 456 is divisible by 6.

11. 11

    Step 11: Consider the number 1

12. 12

    Step 12: Solve the following problem.

Detailed Guide

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