Find the number of prime factors of $(30)^7 \times (22)^5 \times (34)^{11}$
My Work
The prime factorisation of the above number is $2^{34} \times 3^7 \times 5^7 \times 11^5 \times 17^{11}$
Now the number of distinct prime factors of the number is 5.
But total prime factors are=$34+7+7+5+11$
Am I going correct way?