Factors of 17

What is a Factor?

A factor of a number is an integer that divides that number completely, leaving no remainder. For example, 3 is a factor of 18 because when you divide 18 by 3, the result is 6 with no remainder. Other factors of 18 include 1, 2, 6, 9, and 18, since all these numbers divide 18 exactly.

What are the Factors of 17?

Factors of 17 are numbers that can divide 17 without leaving a remainder. Since 17 is a prime number, it has only two factors: 1 and 17.

Also Check: Factors of 12

Pair Factors of 17

Pair factors of 17 are pairs of numbers that, when multiplied together, result in 17. These include both positive and negative pairs:

  • Positive Pair Factor: (1, 17) because 1 * 17 = 17
  • Negative Pair Factor: (-1, -17) because -1 * -17 = 17

Factors of 17 by Division Method

To find the factors of 17 using the division method, divide 17 by different numbers and check for a remainder of zero. If there is no remainder, the number is a factor of 17. Let's check the numbers:

  • 17 ÷ 1 = 17 (Factor: 1, Remainder: 0)
  • 17 ÷ 17 = 1 (Factor: 17, Remainder: 0)

Any other number will leave a remainder when divided into 17. Therefore, the factors of 17 are only 1 and 17.

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Prime Factorization of 17

Prime factorization involves breaking down a number into its prime factors. For 17:

  • Since 17 is a prime number, its only prime factors are 1 and 17.
  • Therefore, 17 = 1 * 17

Also Check: Factors of 144

Solved Examples

Example 1: Determine if 3 is a factor of 17.

Solution: Divide 17 by 3. The result is 5 with a remainder of 2. Hence, 3 is not a factor of 17.

Example 2: List the factors of 17.

Solution: Since 17 is a prime number, its factors are 1 and 17.

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Frequently Asked Questions on Factors of 17

The sum of all factors of 17 is 18. The factors of 17 are 1 and 17, thus their sum is 1 + 17 = 18.

No, 17 is a prime number, so it has only 2 factors: 1 and 17.

Since 17 is a prime number, its factors are 1 and 17.

The prime factorization of 17 is simply 17, as it is a prime number.

The pair factors of 17 that are both positive and negative are (1, 17) and (-1, -17), respectively.