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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).
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Sum of two consecutive odd integers is 244 what is the smallest integer?
The smallest is 121.
What is the smallest number that can be exactly divided by odd numbers?
3, which can be divided by the odd numbers 1 and 3.
If n plus 4 represents an odd integer the next larger number odd integer is represented by?
Every integer is either even (divisible by 2) or odd (not divisible by 2). Since an even number plus 1 is odd and an odd number plus one is even, because 1 does not divide 2. We know (n + 4) is odd. The next integer is (n + 4 + 1) = (n + 5), because an odd number plus 1 is even, (n + 5) is even. The integer after (n + 5) is (n + 6), since (n + 5) we know is even, (n + 6) must be odd. Since (n + 6) is the smallest integer that is greater than (n + 4) and is odd, so (n + 6) is the next odd integer.
Why can an odd number be composite?
Any positive integer with more than two factors is composite.
Three consecutive odd integers have a sum of 45 in algebraci expression?
If x is the smallest odd integer, then x = 2n + 1 for some integer n. Then the next two odd integers are 2n + 3 and 2n + 5 So the question then becomes: 2n+1 + (2n+3) + (2n+5) = 45 or 6n + 9 = 45 to be solved for n and thence the smallest of the three consecutive odd integers.
