Bigger Numbers
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 10 of 58.
With a bigger number, start with the easiest split you can see. 220 ends in 0, so split off a 10: 220 = 22 × 10. Then 22 is 2 × 11 and 10 is 2 × 5. The leaves are 2, 2, 5 and 11, so 220 is 2^2 × 5 × 11.
The divisibility rules from Chapter 1 find the splits for you. An even number gives a 2, a last digit of 0 or 5 gives a 5, and a digit sum that divides by 3 gives a 3. Peel off small primes one at a time, and what is left keeps getting smaller and easier.
A missing leaf works as before, with the powers worked out first. In 2^2 × 5 × n = 220, the known leaves make 4 × 5, which is 20, and 220 / 20 is 11. The missing prime is 11, and that is fine: leaves do not have to be small.
Challenge
The board shows the prime factorization of 120 with one prime missing: 2^3 × 3 × n = 120 (it writes 3 times n as 3n). Find the missing prime n, write the claim n = ..., then press Check.
Try it yourself
Solve for n
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Factors & Fractions
1Factors and Multiples
What a Factor IsFactor PairsDivisibility RulesMultiplesPrime or CompositeRecap: Factors and Multiples4What a Fraction Is
Parts of a WholeFractions on the LineA Fraction of a NumberImproper FractionsRecap: What a Fraction Is7Multiplying Fractions
Top Times TopCancel FirstWhole Times FractionA Fraction of a FractionRecap: Multiplying Fractions10Fractions in Stories
Part of a GroupWhat Is LeftSharing a FractionScaling a RecipeRecap: Fraction Stories2Prime Factorization
Factor TreesUsing ExponentsOne Tree per NumberBigger NumbersRecap: Prime Factorization5Equivalent Fractions
Same Amount, New NameSimplifying FractionsSimplify in StepsComparing FractionsRecap: Equivalent Fractions