Q:
# What are the multiples of 17?

**Multiples of 17 are numbers by which 17 can be exactly divided, such as 34 or 51.** A multiple of 17 is any number that is a product of 17 and an integer.

Because 17 is a large prime number, it can be difficult to recognize patterns among the multiples. When multiplying 17, students should remember that any value they find should be between the similar multiple of 15 and 20. For example, 4 times 15 equals 60 and 4 times 20 equals 80; 4 times 17 equals 68, which is between 60 and 80.

The ones digit of any multiple of 17 follows the 7 times table.

Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.

Multiples of 17 are 17, 34, 51, 68, 85, 102, 119, 136, 153, 170.

Seventeen times any number is equal to the sum of that number multiplied by 10 and 7. In other words, 17*n = n*(10 + 7) = 10*n + 7*n. For example, 17*12 = 12*(10 + 7) = 12*10 + 12*7 = 120 + 84 = 204.

When attempting to find the prime factorization of a multiple of 17, it is easier to start by dividing by smaller, more manageable factors. For example, to find the prime factorization of 272, first divide by 2s.

272/2 = 136

136/2 = 68

68/2 = 34

34/2 = 17

The prime factorization states that 272 = 2*2*2*2*17.

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