A factor of n is a whole number that divides evenly into n — no remainder.
Factors are always ≤ n.
Ask: "Does n ÷ f = whole number?"
4 is a factor of 12 → 12 ÷ 4 = 3 ✓
MULTIPLES
Extend beyond n
A multiple of n is n multiplied by any whole number.
Multiples are always ≥ n.
Ask: "Is m in n's times table?"
36 is a multiple of 12 → 12 × 3 = 36 ✓
Factors are smaller or equal — they fit inside n
|Multiples are larger or equal — they grow beyond n
Every number is both a factor of itself and a multiple of itself.
🔭 Number Explorer
Pick a number (1–100):
💡 Quick Memory Check
Is 7 a factor of 42? 42 ÷ 7 = 6 → Yes ✓
Is 42 a multiple of 7? 7 × 6 = 42 → Yes ✓ (same fact!)
Is 5 a factor of 42? 42 ÷ 5 = 8.4 → No ✗
Is 50 a multiple of 7? 50 ÷ 7 = 7.14… → No ✗
Definition
The Greatest Common Factor is the largest whole number that divides evenly into both numbers.
Your textbook presents three methods — pick whichever fits best!
Step-by-Step GCF Explorer
Number A
&
Number B
Step 0/3
⭐ Relatively Prime!
📐 Key Relationship: GCF × LCM = a × b
—
Definition
The Least Common Multiple is the smallest nonzero whole number that is a multiple of both numbers.
Essential for adding fractions and solving real-world scheduling problems.
Step-by-Step LCM Explorer
Number A
&
Number B
Step 0/3
GCF vs. LCM via Prime Factorization — The Critical Difference
GCF • Only shared primes • Use minimum exponent • Result ≤ both numbers
LCM • All primes from either • Use maximum exponent • Result ≥ both numbers
🚌 Textbook Scenario: The Bus Problem
Two buses stop at the same station — one every 9 minutes, another every 12 minutes.
If they both arrive at noon, when will they next arrive together?
💡 Verify: GCF × LCM = a × b
Practice Score
0
Correct
/
0
Total
Practice Problem
Find the
—
— & —
📝 Worked Solution: Prime Factorization Method
This method works cleanly for any pair. You can verify with Set Intersection or the Euclidean Algorithm.