Question
How many numbers in the range from 200 to 800 are
divisible by 4, 8, and 16?Solution
ATQ;
If a number is a multiple of 4, 8, and 16, then the number is a multiple of the L.C.M of 4, 8, and 16.
L.C.M of 4, 8, and 16 = 16
Smallest multiple of 16 between 200 and 800 = 208
Largest multiple of 16 between 200 and 800 = 784
Common difference = 16
Let the required number of terms be 'n'.
So, 208 + (n - 1) × 16 = 784
Or, n - 1 = (784 - 208) ÷ 16 = 36
So, n = 36 + 1 = 37
So, there are 37 numbers between 200 and 800 which are multiples of 4, 8, and 16.
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