22 X 31
12 isn't a prime factor, since it has 2, 3, 4, & 6 to multiply.
12 = 2 x 2 x 3Alternatively, using power notation:12 = 22 x 32 x 2 x 3 = 12
Factors for 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Factors for 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors for 24 are: 1, 2, 3, 4, 6, 8, 12, 24 Greatest Common Factor is: 12 Alternative method using prime factors: Factorise each number into its prime factors in power format. Greatest common factor is obtained by multiplying the common primes (in all the factorisations) to their lowest power (across the factorisations) together: 24 = 2^3 x 3 36 = 2^2 x 3^2 60 = 2^2 x 3 x 5 Prime 2 occurs in all factorisations, it is a common prime; lowest power is 2^2 Prime 3 occurs in all factorisations, it is a common prime; lowest power is 3 (= 3^1) Prime 5 only occurs in the factorisation of 60, it is not a common prime. greatest common factor = 2^2 x 3 = 12
That's the prime factorization of 140.
22 X 31
It is: 22*5 = 20
5^2 7^1
22 x 11 = 44
3^2 x 11^1
The prime factorization of 668 is 2 x 2 x 167 or 22 x 167 in exponential form.
It is: 2 to the power of 12 = 4096
4554 = 2 * 11 * 23 * 3 * 3 = 2 * 11 * 23 * 32
Digits that are powers of primes are 22 = 4, 23 = 8, and 32 = 9. So, the possible ages now are 44, 48, 49, 84, 88, 89, 94, 98, and 99. Twelve years ago you were a power of a prime, so subtract 12 from each of the numbers and look at them. Powers of primes include 22=4, 23=8, 24=16, 25=32, 26=64, 32=9, 33=27, 34=81, 52=25, and 72=49. 44-12=32, a power of 2 48-12=36, not a power of a prime 49-12=37, not a power of a prime 84-12=72, not a power of a prime 88-12=76, not a power of a prime 89-12=77, not a power of a prime 94-12=82, not a power of a prime 98-12=86, not a power of a prime 99-12=87, not a power of a prime So, 44 fits this part of the question. We could have started with the other part of the question, first. So, if "one year ago you were in your prime" means that it was a prime number, the power of a prime which was 12 years ago should produce a prime number when 11 is added to it. 4+11=15, not a prime 8+11=19, a prime 16+11=27, not a prime 32+11=43, a prime 64+11=75, not a prime 9+11=20, not a prime 27+11=38, not a prime 81+11=92, not a prime 25+11=36, not a prime 49+11=60, not a prime So, the possibilities for one year ago are 19 and 43, meaning the current age is either 20 or 44. The only number that fits the specifications is 44.
It is: 2 to the power of 12 = 4096
the prime factorization of 12 in exponents is 2 to the second power times 3
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