Divisibility Rule of 9
Divisibility Rule of 9
The Rule for 9: The prime factors of 9 are 3 and 3. So we can use a very similar rule to determine if a number is divisible by 9. Basically, we will see if the sum of the digits is divisible by 9. If it is, then the actual number is also divisible by 9. This is done the same way we checked the rule for 3.
In other words, A number is Divisible by 9 , if and only if sum of its digits is divisible by 9.
Illustration 1 : Check whether 495 is divisible by 9 or not ?
Step 1: Add up the digits . 4+9+5=18
Step 2: We know that 18 is divisible by 9.
Illustration 2: Check 871,989 is divisible by 9 or not ?
Step 1: Add up the digits. 8 + 7 + 1 + 9 + 8 + 9 = 42. Step 2: Determine if 9 goes into 42 evenly. We know that 9 x 4 = 36 and 9 x 5 = 45. So 9 will not go into 42 evenly. Step 3: 871,989 is not divisible by 9. Illustration 3: Check ​​​​​​​​​​​​​​92,745 is divisible by 9 or not ?​​​​​​​
Step 1: 9 + 2 + 7 + 4 + 5 = 27 Step 2: 9 goes into 27 3 times because 9 x 3 = 27. Step 3: Because 9 goes into 27 evenly, it also goes into 92,745 evenly. Therefore, 92,745 is divisible by 9.
Consider the following statements and choose the correst option (s) for them. I. A number divisible by 3 is also divisible by 9. II. A number divisible by 3 and by 9, if the sum of all its digits can be divided by 3 and by 9, respectively. | |||
| Right Option : B | |||
| View Explanation |
Which of the following number is not divisible by 9 ? 5463,5949,9840,6507 | |||
| Right Option : C | |||
| View Explanation | |||
Which of the following number is divisible by 9 ? 642,999,888,772 | |||
| Right Option : A | |||
| View Explanation | |||
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