---------------------------------------------------------------------------- Find total number of integers ---------------------------------------------------------------------------- Number of integers from 1 to 100 = 100 There are 100 numbers altogether
---------------------------------------------------------------------------- Find total numbers that can be divided by 2 ---------------------------------------------------------------------------- Number that are multiples of 2 = 100 ÷ 2 = 50 50 of the number are multiples of 2
---------------------------------------------------------------------------- Find total numbers that are multiples of 3 ---------------------------------------------------------------------------- Numbers that are multiples of 3 = 100 ÷ 3 = 33 R 1 33 of the numbers are multiples of 3
Of the 33 numbers that are multiples of 3, half of the numbers are even and had been included in multiples of 2. 33 ÷ 2 = 16 R 1
33 - 16 = 17 17 of the numbers are multiples of 3
---------------------------------------------------------------------------- Total numbers that can be multiples of 2 or 3 ---------------------------------------------------------------------------- 50 + 17 = 67
---------------------------------------------------------------------------- Total number that are neither multiples of 2 nor 3 ---------------------------------------------------------------------------- 100 - 67 = 33
---------------------------------------------------------------------------- Ans: 33 integers are neither multiples of 2 nor multiples 3 ----------------------------------------------------------------------------
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