Numbers have an even number of factors
true or false explain
2007-09-05 09:39:44 · 5 answers · asked by pinoyboy412 1 in Science & Mathematics ➔ Mathematics
False.
A square whole number always has an odd number
of factors.
To see this, decompose n into its prime factors:
n = p_1^a_1 *... p_k^a_k.
Then the number of factors(divisors) of n is
(a_1+1)...(a_k+1).
But if n is a square, all the a_i are even,
so all the factors of (a_1+1)...(a_k+1) are odd.
Examples:
1 1 factor
4 3 factors: 1,2 and 4
9 3 factors: 1,3 and 9
16 5 factors 1,2,4,8 and 16.
2007-09-05 10:13:49 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋
No, because 1 is the only number that can go in to 1.
2007-09-05 16:49:34 · answer #2 · answered by kuszoooo 2 · 0⤊ 0⤋
i think false, not all numbers have an even number of factors.
2007-09-05 16:46:47 · answer #3 · answered by allisoncho7 2 · 0⤊ 0⤋
false if they all had even numbers the factor would never end
2007-09-05 16:47:31 · answer #4 · answered by Anonymous · 0⤊ 1⤋
27 = 3 * 3 * 3
Should be enough to determine the answer
2007-09-05 16:47:55 · answer #5 · answered by dogsafire 7 · 0⤊ 1⤋