22 x 3 = 12
the prime factorization of 12 in exponents is 2 to the second power times 3
2.2.3 and
It is: 60
The largest two-digit number with exactly 12 factors is 96. To determine the number of factors, we can use the formula for the total number of factors based on the prime factorization of a number. The prime factorization of 96 is (2^5 \times 3^1), and using the formula ((e_1 + 1)(e_2 + 1)), where (e_1) and (e_2) are the exponents in the factorization, we find that ( (5+1)(1+1) = 12).
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 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