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The gcf of 35 and z, where z is some unknown positive integer, is 7. There are two possible values for z between 20 and 30. What is the difference between these two values?

User Royson
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Final answer:

To find the two possible values of z, we look for multiples of 7 between 20 and 30, which are 21 and 28. The difference between these two values is 7.

Step-by-step explanation:

The question asks to determine the two possible values for an unknown positive integer z, where the greatest common factor (GCF) of 35 and z is 7, and z lies between 20 and 30. To find the two possible values of z, we can list the multiples of 7 that fall within the specified range, since 7 will need to be a factor of z to have 7 as its GCF with 35.

21 (3×7)

28 (4×7)

The only multiples of 7 between 20 and 30 are 21 and 28. The difference between these two values is 28 - 21 = 7.

User Gertjan Brouwer
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