Factor Tree Worksheet

This worksheet uses the SAGE Notebook to illustrate integer factorization as a product of primes using the ``factor trees'' that students learn about in school.

Factor Tree Worksheet

This worksheet uses the SAGE Notebook to illustrate integer factorization as a product of primes using the ``factor trees'' that students learn about in school.

%hide
print "CLICK ABOVE AND MOVE CURSOR FOR THE SOURCE CODE"
# The source code to draw factorization trees...

import random

def factor_tree(n, font=10):
    rows = []
    v = [(n,None,0)]
    ftree(rows, v, 0, factor(n))
    return draw_ftree(rows, font)

def ftree(rows, v, i, F):
    if len(v) > 0:
        # add a row to g at the ith level. 
        rows.append(v)
    w = []
    for i in range(len(v)):
        k, _,_ = v[i]
        if k is None or is_prime(k):
            w.append((None,None,None))
        else:
            d = random.choice(divisors(k)[1:-1])
            w.append((d,k,i))
            e = k//d
            if e == 1:
                w.append((None,None))
            else:
                w.append((e,k,i))
    if len(w) > len(v):
        ftree(rows, w, i+1, F)

def draw_ftree(rows,font):
    g = Graphics()
    for i in range(len(rows)):
        cur = rows[i]
        for j in range(len(cur)):
            e, f, k = cur[j]
            if not e is None:
                if is_prime(e):
                     c = (1,0,0)
                else:
                     c = (0,0,.4)
                g += text(str(e), (j*2-len(cur),-i), fontsize=font, rgbcolor=c)
                if not k is None and not f is None:
                    g += line([(j*2-len(cur),-i), (k*2-len(rows[i-1]),-i+1)], alpha=0.4, thickness=0.4) 
    return g

def factor_trees(n, cols=4, rows=3, font=10):
    return graphics_array([[factor_tree(n,font) for _ in range(cols)] for _ in range(rows)])

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