Primed and ready

Number Theory Level 1

How many (distinct) prime factors are there in the product 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 ? 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10?

Details and assumptions

There are 2 distinct prime factors in 12, namely 2 and 3.


The answer is 4.

View wiki
Arron Kau by Arron Kau

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

5 solutions

Hatim Khatir
Nov 4, 2013

the prime factors are those which can be divided by only 1 and itself. but it should be noted that 1 is not a prime factor . and the prime factors in the given product are 2,3,5, and 7 . and the required answer is 4.

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Fiyaz
Feb 14, 2014

here only 2, 3, 5 and 7 are the prime number

so these 4 numbers are the prime factors in the above product. Thus, answer is 4

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Sudoku Subbu
Jan 17, 2015

the prime factors are 2,3,5,7 . simple

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Perceba que há 4 números primos(2, 3, 5, 7) em 10!, e que os demais números podem ser escritos como combinação entre os 4 primos.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Devesh Rai
Nov 3, 2013

WE CAN SEE SOME COMPOSITE NUMBERS SUCH AS 4,6,8,9,10. THESE NUMBERS CAN BE ALSO WRITTEN AS THE PRODUCTS OF PRIMES SUCH AS 4 = 2 * 2 , 6 = 2 * 3 , 8 = 2 * 2 * 2 , 9 = 3 * 3 , 10 = 2 * 5 . NOW WE CAN ALSO WRITE IT IN THE FORM OF DISTINCT PRIME FACTORS- 

                    \\\( 2 \\times  8 \\\) *  \\\( 3 \\times 4 \\\)  *  \\\( 5 \\times 2 \\\)  *  7

SO WE CAN SEE THAT DISTINCT PRIME FACTORS ARE 2 , 3 , 5 , 7 . SO THE ANSWER IS 4.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

NOTE THAT WE CAN ALSO SAY IT 10! = 3628800. WE CAN ALSO FIND DISTINCT PRIME FACTORS FROM IT .

Devesh Rai - 7 years, 7 months ago

is there any difference between prime factors and distinct prime factors

Hafsa Maqbool - 7 years, 7 months ago

so funny 2 see plz don't mind sryyyyyy

radha hati - 7 years, 6 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...