Find those prime factors!

How many distinct prime factors does 100100 have?

Details and assumptions

The number 45 = 3 2 × 5 45 = 3^2 \times 5 has 2 distinct prime factors.


The answer is 5.

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11 solutions

Kho Yen Hong
Aug 12, 2013

we know that 100100=1001 x 2^2 x 5^2, then we got three distinct factor. but 1001=10^3 +1=(10+1)(100-10+1)=(10+1)(100-9)=(10+1)(10-3)(10+3)=11 x 7 x 13, so the total number of distinct prime factor is 5

Moderator note:

Nice use of the algebraic identity x 3 + 1 = ( x + 1 ) ( x x + 1 ) x^3 + 1 = (x+1)(x^-x+1) .

eloquent !!

Sufiyan Ghori - 7 years, 10 months ago

nice! factoring really works

rodrigo monte - 7 years, 10 months ago

5 distinc prime number is correct

Tarek Sarker - 7 years, 9 months ago
나 가수
Oct 28, 2013

100100 / 2 = 50050

50050 / 2 = 25025

25025 / 5 = 5005

5005 / 5 = 1001

1001 / 7 = 143

143 / 11 = 13

13 /13 = 1

If you noticed that all of my divisors are unlike prime numbers, So 2^2 x 5^2 x 7 x 11 x 13 = 100100 therefore, we have 5 distinct prime factors. :D

Márko Sálcedo
Aug 13, 2013

100100= (2^2) x (5^2) x (7) x (11) x (13) = 5 distinct prime factors. :)

yap you are right marko

Tarek Sarker - 7 years, 9 months ago
Yf Ooi
Aug 12, 2013

100100=(2^2)(5^2)(7)(11)(13). So there are 5 distinct prime factors.

Kris Kyle
Nov 1, 2013

The Prime Factors of 100100 : 4 • 25 • 7 • 11 • 13

Varsha Jayaraman
Oct 28, 2013

100100=5x20020 =5x5x4004 =5x5x2x2002 =5x5x2x2x1001 =5x5x2x2x11x91 =5x5x2x2x11x7x13 =5^{2} x 2^{2} x 11 x 7 x 13 Therefore, 5, 2,11,7,13 are the 5 distinct prime factors

100100=2^2x5^2x7x11x13 so 2,5,7,11,13 are distinct prime factors of 100100

Sonu Sekar
Oct 28, 2013

The Prime Factors of 100100 : 2 (2) * 5(5 )* 7 * 11 * 13

Steffen Spindler
Oct 28, 2013

2² x 5² x 7 x 11 x 13

Ralph Mcbrown
Aug 17, 2013

100100 = 100 * 1001 = 10 * 10 * 1001 = 5 * 5 * 2 * 2 * 1001 = 5* 5 * 2 * 2 * 143 * 7 = 5 * 5 * 2 * 2 * 13 * 11 * 7

Jaâfar Azizi
Aug 16, 2013

we have 100100 = 2^{2} x 5^{2} x 7 x 11 x 13 than 2 , 5 , 7 , 11 and 13 prime factors does 100100 have. 100100 has 5 distinct prime factors.

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