Using Divisibility Test, Determine Which of the Following Numbers are Divisibly by 4, by 8


Question: Using divisibility test, determine which of the following numbers are divisibly by 4, by 8

(a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159 (f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150

A divisibility rule is a kind of shortcut to figure out if a given integer is divisible by a divisor, without performing the whole division process but by examining its digits.

Answer: The numbers which are divisble by 4 are a), b), c), d), f), g), h) and i) while the numbers divisble by 8 are b),d),f) and h)

The divisibility rule of 4 is: check the last 2 digits of a number and if its divisbile by 4 then the given number is also divisble by 4.

 The divisibility rule of 8 is: check the last 3 digits of a number and if its divisbile by 8 then the given number is divisble by 8.

Explanation:

  1. 572 , last 2 digits - 72, last 3 digits - 572, divisible by 4 but not by 8 as 72 is a multiple of 4 but 572 is not a multiple of 8
  2. 726352 , last 2 digits - 52, last 3 digits - 352, divisible by 4 and by 8 as 52 is a multiple of 4 and 352 is a multiple of 8
  3. 5500 , last 2 digits - 00, last 3 digits - 500, divisible by 4 but not by 8 as 0 is a multiple of 4 but 500 is not a multiple of 8
  4. 6000 , last 2 digits - 00, last 3 digits - 000, divisible by 4 and by 8 as 0 is a multiple of both 4 and 8
  5. 12159 , last 2 digits - 59, last 3 digits - 159, not divisible by 4 and 8 as 59 and 159 are not the multiples of 4 and 8 respectively
  6. 14560 , last 2 digits - 60, last 3 digits - 560, divisible by 4 and by 8 as 60 is a multiple of 4  and 560 is a multiple of 8
  7. 21084 , last 2 digits - 84, last 3 digits - 084, divisible by 4 but not by 8 as 84 is a multiple of 4 but not a multiple of 8
  8. 31795072 , last 2 digits - 72, last 3 digits - 072, divisible by 4 and by 8 as 72 is a multiple of both 4 and 8
  9. 1700 , last 2 digits - 00, last 3 digits - 700, divisible by 4 but not by 8 as 0 is a multiple of 4 but 700 is not a multiple of 8
  10. 2150 , last 2 digits - 50, last 3 digits - 150, not divisible by 4 and 8 as 50 and 150 are not the multiples of 4 and 8 respectively

Thus, the numbers which are divisble by 4 are a), b), c), d), f), g), h) and i) while the numbers divisble by 8 are b),d),f) and h)