| Board | CBSE |
| Textbook | NCERT |
| Class | Class 6 |
| Subject | Maths |
| Chapter | Chapter 3 Playing with Numbers |
Question – 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
Solution –
Divisibility by 4: 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 by 8: A number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8.
(a) Divisibility by 4: The last 2 digits of 572 are 72 which is divisible by 4,
72 ÷ 4 = 18
hence, 572 is divisible by 4.
Divisibility by 8: The last 3 digits of 572 are 572 which is not divisible by 8, hence, 572 is not divisible by 8.
Therefore, 572 is divisible by 4 but not divisible by 8
(b) Divisibility by 4: The last 2 digits of 726352 are 52 which is divisible by 4, hence, 726352 is divisible by 4.
52 ÷ 4 = 13
Hence, 726352 is divisible by 4.
Divisibility by 8: The last 3 digits of 726352 are 352 which is divisible by 8, hence, 726352 is divisible by 8.
Therefore, 726352 is divisible by 4 but not divisible by 8
(c) Divisibility by 4: The last 2 digits of 5500 are 00 which is divisible by 4, hence, 5500 is divisible by 4.
00 ÷ 4 = 0
Hence, 5500 is divisible by 4
Divisibility by 8: The last 3 digits of 5500 are 500 which is not divisible by 8, hence, 5500 is not divisible by 8.
Hence, 5500 is divisible by 4 but not divisible by 8.
(d) Divisibility by 4: The last 2 digits of 6000 are 00 which is divisible by 4, hence, 6000 is divisible by 4.
00 ÷ 4 = 0
Divisibility by 8: The last 3 digits of 6000 are 000 which is divisible by 8, hence, 6000 is divisible by 8.
000 ÷ 8 = 0
Hence, 6000 is divisible by both 4 and 8.
(e) Divisibility by 4: The last 2 digits of 12159 are 59 which is not divisible by 4, hence, 12159 is not divisible by 4.
Divisibility by 8: The last 3 digits of 12159 are 159 which is not divisible by 8, hence, 12159 is not divisible by 8.
Hence, 12159 is not divisible by both 4 and 8.
(f) Divisibility by 4: The last 2 digits of 14560 are 60 which is divisible by 4, hence, 14560 is divisible by 4.
60 ÷ 4 = 15
Divisibility by 8: The last 3 digits of 14560 are 560 which is divisible by 8, hence, 14560 is divisible by 8.
560 ÷ 8 = 70
Hence, 14560 is divisible by both 4 and 8.
(g) Divisibility by 4: The last 2 digits of 21084 are 84 which is divisible by 4, hence, 21084 is divisible by 4.
84 ÷ 4 = 21
Divisibility by 8: The last 3 digits of 21084 are 084 which is not divisible by 8, hence, 21084 is not divisible by 8.
Hence, 21084 is divisible by 4 but not divisible by 8.
(h) Divisibility by 4: The last 2 digits of 31795072 are 72 which is divisible by 4, hence, 31795072 is divisible by 4.
72 ÷ 4 = 18
Divisibility by 8: The last 3 digits of 31795072 are 072 which is divisible by 8, hence, 31795072 is divisible by 8.
072 ÷ 8 = 9
Hence, 31795072 is divisible by both 4 and 8.
(i) Divisibility by 4: The last 2 digits of 1700 are 00 which is divisible by 4, hence, 1700 is divisible by 4.
00 ÷ 4 = 0
Divisibility by 8: The last 3 digits of 1700 are 700 which is not divisible by 8, hence, 1700 is not divisible by 8.
Hence, 1700 is divisible by 4 but not divisible by 8.
(j) Divisibility by 4: The last 2 digits of 2150 are 50 which is not divisible by 4, hence, 2150 is not divisible by 4.
Divisibility by 8: The last 3 digits of 2150 are 150 which is not divisible by 8.
Hence,, 2150 is not divisible by both 4 and 8.
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