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What is complete factorization?
Factorization into its smallest factors.
What is the smallest number with exactly four factors?
Among positive integers, 6
What is the smallest number that has 6 different prime factors?
30,030 Factorization: 2x3x5x7x11x13
What is the least positive integer that has exactly 13 factors?
4096 is the smallest number with exactly 13 factors. (Including 1 and itself as factors).192 is the smallest number with exactly 13 properfactors, (excluding the number itself).120 is the smallest number with at least 13 factors (it has 16 factors)To find the smallest number with exactly N factors (for example, N=12):Factor N into primes, (for example, 12= 2*2*3Subtract 1 from each of the prime factors (for example, 1,1,2)Sort them by largest first (for example, 2,1,1)Raise successive prime numbers to these powers (for example, 2^2,3^1,5^1)Multiply these together (for example: 4*3*5 = 60; 60 is the smallest number with exactly 12 factors).
What is the smallest number that has exactly four factors?
6
What is the prime factorization of the smallest positive integer that has exactly 31 factors?
230
What is the smallest positive integer that has exactly 6 factors?
The smallest positive integer that has exactly 6 factors is 12. To determine the number of factors an integer has, we can use its prime factorization. In the case of 12, its prime factorization is 2^2 * 3, which means it has (2+1)(1+1) = 6 factors.
What is complete factorization?
Factorization into its smallest factors.
What is the smallest number with exactly four factors?
Among positive integers, 6
What is the least positive integer that has exactly eight factors?
The least positive integer that has exactly eight factors is 24. The number of factors of an integer can be determined from its prime factorization. The prime factorization of 24 is (2^3 \times 3^1), and using the formula for the number of factors, ((e_1 + 1)(e_2 + 1)), where (e_i) are the exponents in the factorization, we have ((3 + 1)(1 + 1) = 8). Thus, 24 has exactly eight factors.
What is the third smallest natural number that has exactly four distinct positive factors?
3
What is the smallest number that has 100 different positive integral factors including one and itself?
The smallest number that has exactly 100 different positive integral factors is 2^6 × 3^4. To find the number of factors of a number based on its prime factorization, you can use the formula (e1 + 1)(e2 + 1)...(en + 1), where e1, e2, ..., en are the exponents in the prime factorization. For 2^6 × 3^4, the number of factors is (6 + 1)(4 + 1) = 7 × 5 = 35, which is less than 100, so a different combination of prime factorization would be needed to achieve exactly 100 factors. The correct combination resulting in 100 factors is 2^6 × 3^2 × 5^1, yielding the smallest number, which is 2^6 × 3^2 × 5 = 8640.
What is the sum of the two smallest whole numbers that each has exactly three distinct positive factors?
4 and 9
What is the smallest number that has exactly eight factor?
The smallest number that has exactly eight factors is 24. The factors of 1,2,3,4,6,8,12, and 24
What is the smallest number that has 6 different prime factors?
30,030 Factorization: 2x3x5x7x11x13
What is the smallest natural number that has three distinct prime factors in its factorization?
30
What are the factorization of 293?
The positive integer factors of 293 are: 1, 293
