Factors
Factors is a Grade 6 math skill in Saxon Math, Course 1 that teaches students to identify all whole numbers that divide evenly into a given number with no remainder. Factors always come in pairs: for 24, the factor pairs are (1,24), (2,12), (3,8), and (4,6), giving factors 1, 2, 3, 4, 6, 8, 12, 24. Students find factors systematically by testing divisors from 1 up to the square root of the number. Understanding factors is prerequisite knowledge for finding greatest common factors (GCF), simplifying fractions, and factoring algebraic expressions.
Key Concepts
Contextual Explanation Finding primes one by one is slow. The Sieve method is a genius shortcut where you get rid of all the numbers that aren't prime. It’s like panning for gold—you wash away the dirt (multiples of 2, 3, 5, etc.) to find the valuable gold nuggets (the prime numbers) that remain. Full Example Problem : Use the sieve method to find all prime numbers up to 20. Solution : Step 1 : List numbers 1 20. Cross out 1 (it's not prime). Step 2 : Circle 2. Cross out all other multiples of 2: 4, 6, 8, 10, 12, 14, 16, 18, 20. Step 3 : Circle 3. Cross out its other multiples: 9, 15. Step 4 : Circle 5 and its multiples (already gone). Step 5 : Circle the remaining numbers. The primes are 2, 3, 5, 7, 11, 13, 17, and 19 .
Common Questions
What is a factor in math?
A factor is a whole number that divides another number evenly with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4 with no remainder.
How do you find all the factors of a number?
Test whole numbers starting from 1. If a number divides evenly, both the divisor and the quotient are factors. List factor pairs until both numbers in the pair are the same or the smaller one exceeds the square root.
What are all the factors of 36?
Factor pairs of 36: (1,36), (2,18), (3,12), (4,9), (6,6). All factors listed: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Is every number a factor of itself?
Yes. Any number n is divisible by itself (n ÷ n = 1), so n is always a factor of itself. Also, 1 is always a factor of every number.
How are factors used in simplifying fractions?
To simplify a fraction, find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. For 12/18, GCF is 6, so 12/18 = 2/3.