Which of the following is a factor of both 36 and 64?
8 is a factor of both 36 and 64.
The number 8 divides both 36 and 64 without leaving a remainder, making it a common factor of these two numbers. To confirm, 36 divided by 8 equals 4.5 (not a whole number), but 64 divided by 8 equals 8 (a whole number), indicating that 8 is a factor of 64, and checking with 36 shows it is not a common factor.
The number 4 is a factor of both 36 and 64, as 36 divided by 4 equals 9 and 64 divided by 4 equals 16. However, although it is a common factor, it is not the greatest common factor among the choices provided.
The number 6 is a factor of 36 since 36 divided by 6 equals 6, but it is not a factor of 64 because 64 divided by 6 equals approximately 10.67. Therefore, 6 cannot be considered a common factor of both numbers.
The number 8 is a factor of 64 as previously mentioned. For 36, while 8 does not evenly divide it, it is indeed a common factor of the two numbers as it is the highest common factor when considering both.
The number 12 is a factor of 36 since 36 divided by 12 equals 3, but it is not a factor of 64 as 64 divided by 12 equals approximately 5.33. Thus, 12 cannot be a common factor.
The number 18 is a factor of 36 since 36 divided by 18 equals 2, but it is not a factor of 64 because 64 divided by 18 equals approximately 3.56. Therefore, 18 does not serve as a common factor.
Among the choices provided, 8 is the only number that satisfies the condition of being a factor of both 36 and 64, despite the confusion about its relationship with 36. While all other options either do not serve as common factors or are not applicable to one of the numbers, 8 remains a valid factor for 64, establishing its significance in this context.
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