Mental Factor Trees

Mental Math · Axiom Academy

Learn to break numbers into their prime factors mentally, without writing anything down. Master techniques for finding prime factorizations quickly using mental math strategies. 1. What is a Mental Factor Tree? A factor tree breaks a number into smaller factors until we reach all primes. A mental factor tree means doing this entirely in your head, using smart strategies to make the work easier. The key is recognizing patterns and using divisibility rules to quickly identify factors. Let's start with the simplest strategy! The mental math trick is to always start with the smallest prime factors : 2, 3, 5, and 7. Check them in order until you find one that divides evenly. Mental Strategy: The Small Prime Checklist Check 2: Is it even? If yes, divide by 2. Check 3: Do digits sum to a multiple of 3? If yes, divide by 3. Check 5: Does it end in 0 or 5? If yes, divide by 5. Check 7: Try dividing by 7 if nothing else works. If a number is even , you can immediately divide by 2. Keep dividing by 2 until you get an odd number. This is the fastest mental shortcut! To check if a number is divisible by 3, add up all its digits . If the sum is divisible by 3, then the original number is too! Mental Strategy: The Digit Sum Test 9 is divisible by 3, so 126 is divisible by 3! Check 42: 4 + 2 = 6, divisible by 3! This is the easiest check: if a number ends in 0 or 5 , it's divisible by 5. That's it! 6. Complete Mental Example: 84

This is the written version of the interactive lesson above. See the full Mental Math course.