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# What is the total number of positive integers that are less

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Re: What is the total number of positive integers that are less [#permalink]
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Formula : Number of integers less N and are co-prime to N is given by : N(1-1/a)(1-1/b)(1-1/c).....where a, b, c are prime factors of N..
In the given equation, the prime factors of 100 are 2 and 5. Hence the number will be 100(1-1/2)(1-1/5) = 40.
Hope it helps...
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Re: What is the total number of positive integers that are less [#permalink]
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I did it like this:

There are 50 odd numbers
There are 10 multiples of 5 among those 50 odd numbers

Therefore 50-10 = 40

Could someone confirm if this method is OK

Cheers
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Re: What is the total number of positive integers that are less [#permalink]
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$$100 = 2^2 * 5^2$$

We require to find out numbers which do not have 2 & 5 as factors

Total odd numbers from 1 to 99 = 50 (These do not have 2 as factors)

However the above 50 numbers have 5, 15.... upto 95 (Total =10) factors of 5

Removing the same

50-10 = 40

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Re: What is the total number of positive integers that are less [#permalink]
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eybrj2 wrote:
What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?

A. 30
B. 40
C. 50
D. 60
E. 70

Another way to think about it:

Let's consider numbers from 1 to 100 (since it eases the calculations).

Co-prime with 100 means that they should have no factor of 2 and/or 5.

In the first 100 positive integers, 50 are divisible by 2 (including 100).
So we remove these 50 and are left with 50 numbers not divisible by 2.

Next, in the first 100 numbers, 100/5 = 20 are divisible by 5.
Out of these 20, 10 are even so we have already removed them. We need to remove another 10 with are odd multiples of 5.

We are left with 50 - 10 = 40.

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Re: What is the total number of positive integers that are less [#permalink]
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eybrj2 wrote:
What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?

A. 30
B. 40
C. 50
D. 60
E. 70

100 = 2^2 * 5^2

i.e the Solutions must not contain any factor of 2 and 5 in order to satisfy the given constraints in the question.

Number of multiples of 2 from 1 to 100 = 100/2 = 50

Number of multiples of 5 from 1 to 100 = 100/5 = 20

Number of multiples of 10 from 1 to 100 = 100/10 = 10

So Total number that are multiple of either of 2 or 5 = 50+20-10 = 60

Remaining number = 100 - 60 = 40

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Re: What is the total number of positive integers that are less [#permalink]
how many numbers less than 100 don't have a 2 or 5 as a factor? List out the all the numbers to 50 that work. Once you're half way, you'll notice 20 numbers work. Double that for the "less than 100" goal and you get 40 or b.

1 3 7 9 11 ->5
13 17 19 21 23 -> 10
27 29 31 33 37 -> 15
39 41 43 47 49 -> 20
Re: What is the total number of positive integers that are less [#permalink]
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