Learn by doing · Prime numbers
Every whole number bigger than 1 is built from prime numbers multiplied together. Here you do the building yourself — divide a number down to its primes, split it into a factor tree, group the primes to find every kind of factor, and line up a fraction’s factors to cancel them away.
Type any whole number from 2 to 1,000,000, then work it over in the four sections below — they all start with this number. Blocks uses it too when it’s 100 or less, and there you can also lay out other numbers of your own.
Divide by a prime, then divide the answer, and keep going. Tap a prime below — if it divides evenly, the step counts. If not, nothing breaks; just try another.
Now dividing: 60
Tap any number that isn’t prime and split it into two factors — a line connects it to the two numbers it splits into, like 60 down to 2 and 30. Keep splitting until every branch ends in a prime — those ending numbers are the prime factors.
Any bunch of the prime factors, multiplied together, makes a factor of the whole number. Tap primes to put them in a group, make the group, and a box shows the factor you made and what it pairs with — like 100 = 25 × 4. Every group you make gets its own box.
The number as blocks in a row. Change how many blocks go in each row: if every row comes out the same with nothing left over, that row size is a factor. Leftovers show in red. The numbers across the top count the columns and the numbers down the left count the rows, so you can read off the row × column size at a glance. Works for numbers up to 100.
Across the top: column numbersDown the left: row numbers
Factor pairs you’ve found
My prime collection — 0 of 25 primes up to 100 found
Every time the blocks prove a number prime, add it here. Find all 25 primes up to 100 and the blocks board grows — you’ll be able to use numbers up to 200.
Did you know?
Multiply all 25 primes in your collection together and you get one enormous number:
2,305,567,963,945,518,424,753,102,147,331,756,070
That number is called the primorial of 100, written 100#. It ends in just one zero — the list has only one 2 and one 5, and 2 × 5 = 10.
The whole reduction is one line: your fraction = its prime factors = the reduced fraction. The numerator prime factors sit on the top row, the denominator prime factors on the bottom row. Tap a prime factor in the numerator, then tap the same prime factor in the denominator — the pair cancels, and the reduced fraction at the end of the line changes right away. Cancel every pair you can, and the fraction is in lowest terms.