14 is the GCF of a number M and 210. What are the possible values of M?
Answer (2)
The question asks us to find possible values of a number M given that its greatest common factor (GCF) with 210 is 14. The GCF of two numbers is the largest number that divides both numbers without leaving a remainder. Since 14 is the GCF of M and 210, M must be a multiple of 14. To find such multiples, remember that 210 is 14 multiplied by 15, therefore any multiple of 14 that is less than or equal to 210 will be a factor of 210. For example, 14, 28, 42, ... up to 210 are all multiples of 14. Additionally, since the problem does not limit how large M can be, any number larger than 210 that is a multiple of 14 can also be a value for M (such as 224, 238, etc.). One way to express the possible values of M is by using the set notation {M | M = 14k, k is a positive integer}.
The possible values of M are any multiples of 14, as 14 is the GCF with 210. This includes values such as 14, 28, 42, and so on, up to any integer multiple of 14. Examples can range from the smallest 14 to larger numbers like 224, 238, etc.
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