How can the whole number 378 be expressed as a product of prime numbers with exponents?(1 point)Responses2⋅27⋅72 times 27 times 72⋅33⋅72 times 3 cubed times 72⋅3⋅3⋅3⋅72 times 3 times 3 times 3 times 714⋅2714 times 27
The prime factorization of 378 is expressed as:
2 * 3 * 3 * 3 * 7 * 7
Find the GCF of 18j+27.(1 point)Responses18185454339
To find the GCF (Greatest Common Factor) of 18j+27, we need to factor both terms and find the product of the common factors, taking their lowest exponent.
The factors of 18j are:
2 * 3 * j
The factors of 27 are:
3 * 3 * 3
The common factors between 18j and 27 are:
3 * 3
Therefore, the GCF of 18j and 27 is 9.
Find the GCF of 42m−28n.(1 point)Responses14148484772
To find the GCF (Greatest Common Factor) of 42m - 28n, we need to factor both terms and find the product of the common factors, taking their lowest exponent.
The factors of 42m are:
2 * 3 * 7 * m
The factors of 28n are:
2 * 2 * 7 * n
The common factors between 42m and 28n are:
2 * 7
Therefore, the GCF of 42m and 28n is 14.
Use properties of operations to factor 8w + 16 using the GCF. (1 point)Responses2(4w + 8)2 Left Parenthesis 4 w plus 8 Right Parenthesis4(2w + 4)4 Left Parenthesis 2 w plus 4 Right Parenthesis6(2w + 10)6 Left Parenthesis 2 w plus 10 Right Parenthesis8(w + 2)
To factor 8w + 16 using the GCF (Greatest Common Factor), we need to find the greatest common factor of the two terms.
The factors of 8w are:
2 * 2 * 2 * w
The factors of 16 are:
2 * 2 * 2 * 2
The common factors between 8w and 16 are:
2 * 2 * 2
Therefore, the GCF of 8w and 16 is 8.
We can then factor out the GCF from both terms:
8w + 16 = 8(w + 2)
Therefore, using the GCF, we can factor 8w + 16 as 8(w + 2).
Factor −27h + 6 using the GCF. (1 point)Responses3(−9h + 2)3 Left Parenthesis negative 9 h plus 2 Right Parenthesis3(9h − 2)3 Left Parenthesis 9 h minus 2 Right Parenthesis3(9h + 2)3 Left Parenthesis 9 h plus 2 Right Parenthesis3(−9h − 2)
To factor -27h + 6 using the GCF (Greatest Common Factor), we need to find the greatest common factor of the two terms.
The factors of -27h are:
-1 * 3 * 3 * h
The factors of 6 are:
2 * 3
The common factor between -27h and 6 is 3.
We can then factor out the GCF from both terms:
-27h + 6 = 3(-9h + 2)
Therefore, using the GCF, we can factor -27h + 6 as 3(-9h + 2).