the prime factorization of 12 in exponents is 2 to the second power times 3
2.2.3 and
It is: 60
Write the prime factorization with exponents. Add 1 to each exponent. (Numbers without exponents actually have the exponent 1.) Multiply them together. That will be the number of factors. 10 = 2 x 5 = 21 x 51 2 x 2 = 4 10 has four factors. 72 = 23 x 32 4 x 3 = 12 72 has twelve factors. Square numbers can be tricky. The prime factorization of 9 should be written as 32, not 3 x 3. Adding 1 to the 2 gives you 3. 9 has three factors.
The prime factorization of 10,800 using exponents is 2^4 x 3^3 x 5^2 10800 / \ 108 x 100 / \ / \ 12*9 x 5*10 / \ \ \ /\ 6*2*9 x 5*5*2 /\ / \ \ \ \ 3*2*2*9 x 5x5x2 3x2x2x9x5x5x2
the prime factorization of 12 in exponents is 2 to the second power times 3
22 x 3 = 12
2^2*3 = 12 2*3^2 = 18
2.2.3 and
12 = 2 x 2 x 3
24=2*12=2*2*6=2*2*2*323*3
144 is a perfect square, whose square factor is 12: Therefore we simply repeat the prime factorization of 12 (3,2,2) twice: 2,2,2,2,3,3.
the prime facotrization of 154 is 12 times 3 times 5
12 = 22 x 31
It is: 60
12 2X6 2X2X3 22X31
22 x 3