Is 8 a factor of 64r + 52? Choices: (A)yes (B)no

Factor out greatest common factor: Simplify the expression by factoring out the greatest common factor, which is 4. 64r + 52 = 4(16r + 13) Check divisibility by 8: Check if 8 is a factor of the simplified expression 4(16r + 13). Since 4 is not divisible by 8, the entire expression 4(16r + 13) cannot be divisible by 8 unless (16r + 13) is divisible by 2. Check divisibility by 2: Check if (16r + 13) is divisible by 2. Since 16r is always divisible by 2 (because 16 is even), we need to check if 13 is divisible by 2. 13 is not divisible by 2, hence (16r + 13) is not divisible by 2.

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Is $8$ a factor of $64r + 52$ ? $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Math Problems

Grade 8

Factors of linear expressions

Full solution

Q. Is

8

a factor of

64r + 52

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Factor out greatest common factor: Simplify the expression by factoring out the greatest common factor, which is $4$ . $64r + 52 = 4(16r + 13)$
Check divisibility by $8$ : Check if $8$ is a factor of the simplified expression $4(16r + 13)$ . $\newline$ Since $4$ is not divisible by $8$ , the entire expression $4(16r + 13)$ cannot be divisible by $8$ unless $(16r + 13)$ is divisible by $2$ .
Check divisibility by $2$ : Check if $(16r + 13)$ is divisible by $2$ . $\newline$ Since $16r$ is always divisible by $2$ (because $16$ is even), we need to check if $13$ is divisible by $2$ . $\newline$ $13$ is not divisible by $2$ , hence $(16r + 13)$ is not divisible by $2$ .