Which of the following numbers has the largest number of unique prime factors?:
{135, 62, 96}

Question

Noah Archer · Accepted Answer

#96# has the largest number of unique prime factors.

Prime factors of #135# are #3# and #5# as #135=3xx3xx3xx5# Prime factors of #62# are #2# and #31# as #62=2xx31# Prime factors of #96# are #2# and #3# as #96=2xx2xx2xx2xx2xx3# Hence, all these numbers have just two prime numbers as factors, but #96# has the largest number of unique prime factors.

Genesis Amaya · Answer

undefined To determine which number has the largest number of unique prime factors among {135, 62, 96}, we need to factorize each number into its prime factors and count the unique primes.

1. For 135:
   Prime factorization: $135 = 3 \times 3 \times 3 \times 5$
   Unique prime factors: 3, 5
   Total unique prime factors: 2

2. For 62:
   Prime factorization: $62 = 2 \times 31$
   Unique prime factors: 2, 31
   Total unique prime factors: 2

3. For 96:
   Prime factorization: $96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3$
   Unique prime factors: 2, 3
   Total unique prime factors: 2

Comparing the results, we see that 135 has the largest number of unique prime factors, with 2 unique primes (3 and 5). Therefore, the answer is 135.

Which of the following numbers has the largest number of unique prime factors?: {135, 62, 96}