How many prime factors in 25^10 * 36^10 * 20^10 ?

• 25^10 * 36^10 * 20^10
  =(5*5)^10 * (2*2*3*3)^10 * (2*2*5)^10
  =(5^10 * 5^10) * (2^10 * 2^10 * 3^10 * 3^10) * (2^10 * 2^10 * 5^10)
  =5^30 * 2^40 * 3^20
  
  number of distinct prime factors = 3
  number of prime factors = 30+40+20 = 90
• 10 years agoHelpfull: Yes(10) No(0)
• 25^10* 36^10* 20^10
  = (5*5)^10 *(3*3*2*2)^10 * (5*2*2)^10
  = 5^10 * 5^10 * 3^10 * 3^10 * 2^10* 2^10 * 5^10 * 2^10 * 2^10
  so, total number of prime factors= 10*9= 90
• 10 years agoHelpfull: Yes(2) No(0)
• 5^20 * 3^20 * 2^20 * 2^10 * 2^10 * 5^10
  so 20+20+20+10+10+10=90
• 10 years agoHelpfull: Yes(1) No(0)