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krek1111 [17]
3 years ago
5

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

Mathematics
1 answer:
julia-pushkina [17]3 years ago
8 0
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Find total number of integers
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Number of integers from 1 to 100 = 100
There are 100 numbers altogether

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Find total numbers that can be divided by 2
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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

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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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