Q1. Using the test of divisibility, find which of the following numbers are divisible by 3?
Answer:
Note: A number is divisible by , if the sum of the digits of the number is divisible by .

 Sum of is divisible by . Hence is divisible by .

 Sum of . is not divisible by . Hence is divisible by .

 Sum of . is divisible by . Hence is divisible by .

 Sum of . is divisible by . Hence is divisible by .

 Sum of . is divisible by . Hence is divisible by .
Which of the above numbers are divisible by 9?
Note: A number is divisible by if the sum of the digits of the number is divisible by .
 Therefore, and are divisible by .
Q2. Using the test of divisibility, find which of the following numbers are divisible by 3?
Which of the above numbers are divisible by 6?
Answer:
 Note: A number is divisible by , if the sum of the digits of the number is divisible by .
 Note: A number is divisible by , if the last digit of the number is , and .
 Note: A number is divisible by , if it is divisible both by and .

 Sum of . 26 $ is not divisible by . Hence is not divisible by . It is divisible by .

 Sum of is divisible both by and . Hence the number is also divisible by .

 Sum of is divisible by but not by . Hence the number is not divisible by .

 Sum of is divisible by but not by . Hence the number is not divisible by .

 Sum of is divisible by and . Hence the number is also divisible by .

 Sum of is divisible by but not by . Hence the number is not divisible by .
Q3. Using the test of divisibility, find which of the following numbers are divisible by 4?
Which of the above numbers are divisible by $latex 8?
Answer:
Note:
 A number is divisible by if the number formed by the last two digits of the number is divisible by .
 A number is divisible by if the number formed by then last three digits of the number is divisible by

 is not divisible by . Hence the is not divisible by .
 is not divisible by . Hence the is not divisible by .

 is not divisible by . Hence the is not divisible by .
 is not divisible by . Hence the is not divisible by .

 is divisible by . Hence the is divisible by .
 is divisible by . Hence the is divisible by .

 is not divisible by . Hence the is not divisible by .
 is not divisible by . Hence the is not divisible by .

 is divisible by . Hence the is divisible by .
 is divisible by . Hence the is divisible by .

 is divisible by . Hence the is divisible by .
 is divisible by . Hence the is divisible by .
Q4. Which of the above numbers are divisible by 6?
Answer:
Note:
 A number is divisible by , if the sum of the digits of the number is divisible by .
 A number is divisible by , if the last digit of the number is , and .
 A number is divisible by , if it is divisible both by and .

 Sum of is divisible by . Hence is divisible by .
 The last digit is which is not divisible by .
 Hence the number is not divisible by .

 Sum of is divisible by . Hence is divisible by .
 The last digit is which is divisible by .
 Hence the number is divisible by .

 Sum of is divisible by . Hence is divisible by .
 The last digit is which is divisible by .
 Hence the number is divisible by .

 Sum of is divisible by . Hence is divisible by .
 The last digit is which is divisible by .
 Hence the number is divisible by .

 Sum of is divisible by . Hence is divisible by .
 The last digit is which is not divisible by .
 Hence the number is not divisible by .

 Sum of is not divisible by . Hence is divisible by .
 The last digit is which is not divisible by .
 Hence the number is not divisible by .
Q5. Which of the above numbers are divisible by ?
Answer:
Note: A number is divisible by id the difference between the sum of its digits at odd places and the sum of the digits at even places is either 0 or a number divisible by .

 Difference = (sum of digits at odd places) – (sum of digits at even places) .
 is not divisible by . Hence then number is not divisible by .

 Difference = (sum of digits at odd places) – (sum of digits at even places) .
 is not divisible by . Hence then number is not divisible by .

 Difference = (sum of digits at odd places) – (sum of digits at even places)
 is divisible by . Hence then number is divisible by .

 Difference = (sum of digits at odd places) – (sum of digits at even places)
 is no divisible by . Hence then number is not divisible by .

 Difference = (sum of digits at odd places) – (sum of digits at even places)
 Hence then number is divisible by .

 Difference = (sum of digits at odd places) – (sum of digits at even places)
 Hence then number is divisible by .
Thank you,
This amazing post has helped me expand my knowledge on factors and Multiples.
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