**Educational Text with True/False Table**| Statement | T | F ||---------------------------------------------------------------------------------------------------------------------------------------------------|-----|-----|| The larger the number, the more factors it has. | | || 10|5 | | || The prime factorization of 600 = 2×3×10² | | || For all integers, x³ = x|x²| | | || For all integers, |−x + −y| = |x + y| | | || Multiplying negative numbers is commutative and associative | | || The greatest common multiple for any two numbers can be found by multiplying the two numbers together. | | |**Instructions:**- Mark each statement with "T" for true and "F" for false based on mathematical knowledge.- Evaluate each mathematical statement carefully to determine its validity.- After marking, explain the reasons for your choice if possible.

Greatest common Multiple is Highest common factor of two numbers. The Multiplying any two negative number the result is always positive. Commutative Properties of Multiplication : Let A and B are two numbers then A·B=B·A Associative Properties of Multiplication : Let A,B and C are three numbers then A·(B·C)=(A·B)·C1. Let us consider any larger number 233 it has only factor 1 and 233 . Thus, Larger the number does not means more number of factors The statement is False. 2. Let us consider the given expression 10|5 which is read as 10 divides 5 which is not correct as 5 divides 10 The statement is False. 3. Let us consider the number 600, the prime factorization of 600 is 600=2x2x2x3x5x5 The given prime factorization is 600=2x3x102 here 10 is not a prime number The statement is False 4. Let us consider the equation , for all integers x, x3=x|x2| Since x2=|x2| thus, the expression is correct The statement is True 5. For all the integer x, y , |-x+-y|=|-(x+y)|=|x+y The statement is True 6. Let us consider any two negative number say -x, -y where x,y>0 Now, (-x)(-y)=xy=yx=(-y)(-x) Thus, Multiplication of two negative number is commutative Let us consider the negative number -x,-y, -z where x,y,z>0 (-x)[(-y)(-z)]=(-x)[yz]=-xyz=(-x)(-y)(-z)=[(-x)(-y)](-z) Thus, Multiplication of two negative numbers is associative The statement is True. 7. Greatest common multiple for any two number is the greatest multiple of both the number A and B that divides both A and B . Thus, the Greatest common multiple is the highest common factor which is not the product of the tow numbers The statement is False.