For positive integers, it is true that the largest factor of any number is itself
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False. If s is a factor of 16, then the greatest common factor (GCF) of s and 16 would be s, not 16. The GCF is the largest number that divides both numbers evenly, and in this case, that number would be s, the smaller of the two factors.
D is the choice that is not true.
No. The opposite is true: the gcf of an odd number and an even number is always odd. All the factors of an odd number are odd; or to put it another way: If a number has an even factor, the number itself must be even. Thus the only common factors between odd and even numbers must be odd.
The statement that the rank of product of two matrices cannot exceed the rank of either factor is a true statement. The rank of a matrix is the largest number of linearly independent rows or columns. The column rank is equal to the row rank in every matrix.
False. Factors divide evenly with no remainder.