Finding Factors of a Number: A Comprehensive Guide with Flashcards

Introduction to Factors

Finding the factors of a number means identifying all the whole numbers that can be multiplied together to produce that number. For instance, the factors of 120 include 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Starting with the Basics

1. Identifying 1 and the Number Itself: All whole numbers are divisible by 1 and the number itself. Thus, for 120, both 1 and 120 are factors.

2. Checking for Divisibility:By 2: Since 120 is even, it’s divisible by 2. Calculating 120÷2=60120 \div 2 = 60120÷2=60 gives us factors 2 and 60.
   By 3: Adding the digits of 120 (1 + 2 + 0 = 3), which is divisible by 3. Thus, 120÷3=40120 \div 3 = 40120÷3=40 yields factors 3 and 40.
   By 4: The last two digits of 120 form 20, which is divisible by 4. Hence, 120÷4=30120 \div 4 = 30120÷4=30 gives us factors 4 and 30.
   By 5: Since 120 ends in 0, it’s divisible by 5. Thus, 120÷5=24120 \div 5 = 24120÷5=24 provides factors 5 and 24.
   By 6: Divisible by both 2 and 3, so 120÷6=20120 \div 6 = 20120÷6=20 gives us factors 6 and 20.
   By 8: Checking 120÷8=15120 \div 8 = 15120÷8=15, we find factors 8 and 15.
   By 10: Ending in 0 means 120÷10=12120 \div 10 = 12120÷10=12, giving factors 10 and 12.
   

Verifying Higher Numbers

• Checking for 7 and 9: Neither divide 120 evenly, so they are not factors.

• Up to 11: 11 does not divide 120 evenly either.

Comprehensive List of Factors

After verification, the complete list of factors for 120 includes: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Understanding how to find factors not only helps in arithmetic but also lays the groundwork for more complex mathematical concepts. For a detailed walkthrough, don't miss the Khan Academy video embedded above.