How many integers from 1 through 100 are neither multiples of 2 nor multiples of 3 ?

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