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What is the smallest number that has exactly nine factors?
36. (Factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36.)
What are the factors of 6 and 3?
Factors of 6 1,2,3,6 Factors of 3 1,3 (this mean that 3 is a prime number)
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 next number after 6 that has exactly four factors?
There is no such number. Any prime number raised to the third power has exactly four factors. For example, 23 = 8; its factors are 1, 2, 4, 8 (1, 2, 22, 23). Since - as is well-known - there is no largest prime number, there is no largest number that has exactly four factors.
Why is 64 the least number that has 7 factors?
The number 64 is the least number that has exactly 7 factors because it is a perfect power of a prime, specifically (2^6). The number of factors of a number can be determined using the formula ((e_1 + 1)(e_2 + 1)...(e_n + 1)), where (e_i) are the exponents in its prime factorization. For 64, the factorization is (2^6), leading to ((6 + 1) = 7) factors. Smaller numbers either have fewer factors or do not meet the requirement of having exactly 7.
What is the smallest number that has exactly 4 factors?
6. Factors are 1, 2, 3, and 6.
What is the least whole number with exactly 4 different factors?
If you disregard 1 and the number itself, then 12, with the factors 2, 3, 4 and 6. If you include 1 and the number itself, then 6 with factors 1, 2, 3 and 6.
Is 3 and 6 prime numbers?
A prime number is a number with exactly two distinct factors: itself and oneThe only factors of 3 are 1 and 3 so it is a prime number.The factors of 6 are 1,2,3 and 6 which has more than two factors so it is not a prime number.
When you divide a number exactly by another number the which number become factors of that number?
6 divides 54 exactly to yield 9. Then 6 and 9 are factors of 54.
What is the smallest number that has exactly four factors?
6
What is the smalest number with exactly 4 factors?
6
What is the smallest number with exactly 6 factors?
12
What is the smallest number with exactly 4 factors?
6
What is the largest two digit number with exactly 6 factors?
How about 99 whose factors are: 1, 3, 9, 11 33 and 99
What is the least number with exactly 8 factors?
Oh, dude, the least number with exactly 8 factors is 24. It's like, got factors 1, 2, 3, 4, 6, 8, 12, and 24. So, yeah, that's the magic number with just the right amount of factors to make it cool.
What is the smallest odd integer with exactly 6 factors?
The smallest odd integer with exactly 6 factors is 945. This number can be expressed as (3^3 \times 5^1 \times 7^1). The number of factors is calculated using the formula ((e_1 + 1)(e_2 + 1)(e_3 + 1)), where (e_i) are the exponents in the prime factorization. For 945, the factors count is ((3+1)(1+1)(1+1) = 4 \times 2 \times 2 = 16), so we need to adjust to find the correct configuration. The correct number with exactly 6 factors is (3^5), which equals 243, as it has factors calculated as ((5+1) = 6).
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.
