Definition: A natural number is a factor of a whole number if it divides into it evenly (no remainder).

Rule: The number 1 and the number itself are always factors of a natural number. Notes
  • Factors and prime numbers are positive integers (natural numbers). This is a standard convention.
  • So: 1 and the absolute value of the number are always factors of a whole number. For example: 1 and 5 are factors of -5.
Demonstration for factors

4th-6th Grade: Factors of numbers <50

Step 1: Divide the number by all the prime numbers less than "half of number" until we get to a prime.
        If none of these primes divide, the number itself is prime.
Step 2: The factors are: 1, the number itself and all of the combinations of the prime factors.
  1. Find the factors of 28. Mathcast Answer: 1, 2, 4, 7, 14, 28
  2. Find the factors of 33. Mathcast Answer: 1, 3, 11, 33
  3. Find the factors of 47. Mathcast Answer: 1, 47 (47 is a prime number.)

7th Grade & up: See Prime Factorisation

Rule: (a,b) is a factor pair of d if a \cdot b=d . Notes

  • (a,b) is the same factor pair as (b,a).
  • Factor pairs are found for positive integers (since factors are positive integers).
Demonstration for factor pairs

  Find all of the factor pairs of the number 35

1. The factors of 35 are 1, 5, 7 and 35.
2. The factor pairs of 35 are (1,35) and (5,7)

  Find all the factor pairs of 63.

1. The factors of 63 are 1, 3, 7, 9, 21 and 63.
2. The factor pairs of 63 are (1,63), (3,21) and (7,9).

  Find all the factor pairs of 41.

1. The factors of 41 are 1 and 41. (41 is a prime number).
2. The factor pairs of 41 are (1,41).

  Find all the factor pairs of 64.

1. The factors of 64 are 1, 2, 4, 8, 16, 32 and 64.
2. The factor pairs of 41 are (1,64), (2,32), (4,16) and (8,8).
Standards for 4th-6th grade: CA 4.NS.4.0, CA 5.NS.1.4, ACT Number Sense 20-23
Standards for 7th grade & up: ACT Number Sense 24-28

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Page last modified on January 06, 2009, at 11:29 AM