Which of the following numbers has the largest number of unique prime factors?:
{78, 217, 74, 420}

Question

Mila Anderson · Accepted Answer

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

Prime factors of #78# are #2#, #3# and #13# as #78=2xx3xx13# Prime factors of #217# are #7# and #31# as #217=7xx31# Prime factors of #74# are #2# and #37# as #74=2xx37# Prime factors of #420# are #2#, #3#, #5# and #7# as #420=2xx2xx3xx5xx7# Hence, #420# has the largest number of unique prime factors.

Levi Adams · Answer

undefined To find the number with the largest number of unique prime factors among {78, 217, 74, 420}, let's calculate the prime factorization of each number:

1. For 78: $78 = 2 \times 3 \times 13$
2. For 217: $217 = 7 \times 31$
3. For 74: $74 = 2 \times 37$
4. For 420: $420 = 2^2 \times 3 \times 5 \times 7$

Now, let's count the unique prime factors for each number:

1. For 78: 3 unique prime factors (2, 3, 13)
2. For 217: 2 unique prime factors (7, 31)
3. For 74: 2 unique prime factors (2, 37)
4. For 420: 4 unique prime factors (2, 3, 5, 7)

Thus, among the given numbers, 420 has the largest number of unique prime factors, which is 4.

Which of the following numbers has the largest number of unique prime factors?: {78, 217, 74, 420}