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Is 88 a factor of 64r+5264r + 52?\newlineChoices:\newline(A)yes\newline(B)no

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Full solution

Q. Is 88 a factor of 64r+5264r + 52?\newlineChoices:\newline(A)yes\newline(B)no
  1. Factor out greatest common factor: Simplify the expression by factoring out the greatest common factor, which is 44.64r+52=4(16r+13)64r + 52 = 4(16r + 13)
  2. Check divisibility by 88: Check if 88 is a factor of the simplified expression 4(16r+13)4(16r + 13).\newlineSince 44 is not divisible by 88, the entire expression 4(16r+13)4(16r + 13) cannot be divisible by 88 unless (16r+13)(16r + 13) is divisible by 22.
  3. Check divisibility by 22: Check if (16r+13)(16r + 13) is divisible by 22.\newlineSince 16r16r is always divisible by 22 (because 1616 is even), we need to check if 1313 is divisible by 22.\newline1313 is not divisible by 22, hence (16r+13)(16r + 13) is not divisible by 22.

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