Question

How many numbers less than 10000 have an even number of factors?​

Answer 1

Answer:

The number 10000 has 23 factor not counting 1 or itself makeing it a square and maybe composite. Prime Factors for the number 10000 = (24 × 54) or(2 × 2 × 2 × 2 × 5 × 5 × 5 × 5).

Step-by-step explanation:

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Answer 2

There are 19 integers less than 10000 that have an even number of factors.

Given

Factors of 10000.

To find

The No. of Even numbers less than factors of  10000.

Solution

Factors of 10000,

10000/1 = 10000

10000/2=5000

10000/4=2500

10000/5=2000

10000/8=1250

10000/10=1000

10000/16=625

10000/20=500

10000/25=400

10000/40= 250

10000/50=200

10000/80=125

10000/ 100=100

10000/125=80

10000/ 200=50

10000/ 250= 40

10000/400=25

10000/500=20

10000/ 625=16

10000/1000=10

10000/ 1250=8

10000/ 2000=5

10000/2500=4

10000/ 5000=2

10000/10000= 1

(Positive numbers that divide 10000 without leaving a remainder).

∴25 integers are there for the Factors of 10000.

Writing the even number from the factors of 10000,

Even number⇒ Numbers that can be exactly divisible by 2.

2, 4,  8, 10, 16, 20, 40, 50, 80, 100,  200, 250, 400, 500, 1000, 1250, 2000, 2500, 5000, 10000.

(Now we excluding 10000 because in the question they ask for less than 10000.)

We get,

2, 4,  8, 10, 16, 20, 40, 50, 80, 100,  200, 250, 400, 500, 1000, 1250, 2000, 2500, 5000.

Hence,There are 19 integers.  

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