1. Using divisibility tests, determine which of the following numbers are divisible by 2;
by 3; by 4; by 5; by 6; by 8; by 9; by 10 ; by 11 (say, yes or no):
Answer:
2. Using divisibility tests, determine which of the following numbers are divisible by
4; by 8:
(a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159
(f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150
Answer:
3. Using divisibility tests, determine which of following numbers are divisible by 6:
(a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352
(f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852
Answer:
4. Using divisibility tests, determine which of the following numbers are divisible by 11:
(a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001
(f) 901153
Answer:
5. Write the smallest digit and the greatest digit in the blank space of each of the following
numbers so that the number formed is divisible by 3 :
(a) __ 6724 (b) 4765 __ 2
Answer:
6. Write a digit in the blank space of each of the following numbers so that the number
formed is divisible by 11 :
(a) 92 __ 389 (b) 8 __ 9484
by 3; by 4; by 5; by 6; by 8; by 9; by 10 ; by 11 (say, yes or no):
Number  Divisible by  
2  3  4  5  6  8  9  10  11  
128  Yes  No  Yes  No  No  Yes  No  No  No 
990  ....  ....  ....  ....  ....  ....  ....  ....  .... 
1586  ....  ....  ....  ....  ....  ....  ....  ....  .... 
275  ....  ....  ....  ....  ....  ....  ....  ....  .... 
6686  ....  ....  ....  ....  ....  ....  ....  ....  .... 
639210  ....  ....  ....  ....  ....  ....  ....  ....  .... 
429714  ....  ....  ....  ....  ....  ....  ....  ....  .... 
2856  ....  ....  ....  ....  ....  ....  ....  ....  .... 
3060  ....  ....  ....  ....  ....  ....  ....  ....  .... 
406839  ....  ....  ....  ....  ....  ....  ....  ....  .... 
Answer:
Number  Divisible by  
2  3  4  5  6  8  9  10  11  
128  Yes  No  Yes  No  No  Yes  No  No  No 
990  Yes  Yes  No  Yes  Yes  No  Yes  Yes  Yes 
1586  Yes  No  No  No  No  No  No  No  No 
275  No  No  No  Yes  No  No  No  No  Yes 
6686  Yes  No  No  No  No  No  No  No  No 
639210  Yes  Yes  No  Yes  Yes  No  No  Yes  Yes 
429714  Yes  Yes  No  No  Yes  No  Yes  No  No 
2856  Yes  Yes  Yes  No  Yes  No  No  No  No 
3060  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  No 
406839  No  No  No  No  No  No  No  No  No 
2. Using divisibility tests, determine which of the following numbers are divisible by
4; by 8:
(a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159
(f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150
Answer:
Using divisibility tests: A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4. Divisibility for 1 or 2 digit numbers by 4 has to be checked by actual division.  Numbes Divisible by 4:

Using divisibility tests:a number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8. The divisibility for numbers with 1, 2 or 3 digits by 8 has to be checked by actual division.  Numbes Divisible by 8:

(a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352
(f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852
Answer:
Using divisibility tests: Divisiblity by 6 : if a number is divisible by 2 and 3 both then it is divisible by 6 also. Divisiblity by 2 : A number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place. Divisiblity by 3 :If the sum of the digits is a multiple of 3, then the number is divisible by 3.
 Numbers Divisible by 6:

(a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001
(f) 901153
Answer:
Using divisibility tests: Divisiblity by 11 : To check the divisibility of a number by 11, the rule is, find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number.If the difference is either 0 or divisible by 11, then the number is divisible by 11.
 Numbers Divisible by 11:

numbers so that the number formed is divisible by 3 :
(a) __ 6724 (b) 4765 __ 2
Answer:
Number divisible by 3 Using Smallest digit  Number divisible by 3 Using Greatest digit  
(a) __ 6724  26724  86724 
(b) 4765 __ 2  476532  476592 
formed is divisible by 11 :
(a) 92 __ 389 (b) 8 __ 9484
Answer:  Numbers divisible by 11 Using a digit in blank space 
(a) 92 __ 389  924389 
(b) 8 __ 9484  869484 
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