Number programs

Part of the free LogicWiz Python course, Module 2: Decisions and loops. The examples and practice run in the app.

Board papers and placement tests keep asking the same six: prime, factorial, Fibonacci, GCD, Armstrong, palindrome. Underneath, they are all a loop plus % and //.

You'll learn to

• Peel off digits with % 10 and // 10
• Write prime, factorial, Fibonacci and GCD/LCM programs
• Check Armstrong numbers and number palindromes
• Use a trace table to catch off-by-one bugs

Learn

Peeling digits

n = 472
while n > 0:
    d = n % 10
    print(d)
    n = n // 10

n % 10 is the last digit. n // 10 drops the last digit. Repeat until nothing is left. This one loop is the heart of digit sum, reverse, palindrome and Armstrong.

A trace table

Board examiners love trace tables. For the loop above with n = 472:

After round 3, n > 0 is False and the loop stops. When your program is wrong, make this table by hand: the bad row shows the bug.

Reverse a number, check palindrome

n = 1221
rev = 0
t = n
while t > 0:
    rev = rev * 10 + t % 10
    t = t // 10
print(rev)
print("Palindrome" if rev == n else "Not palindrome")

rev * 10 shifts the digits left to make room, then the new last digit goes in. We work on a copy t so the original n survives for the comparison at the end.

Armstrong numbers

n = 153
k = len(str(n))
s = 0
t = n
while t > 0:
    s += (t % 10) ** k
    t //= 10
print(n, k, s, s == n)

An Armstrong number equals the sum of its digits, each raised to the number of digits: 1³ + 5³ + 3³ = 153. len(str(n)) counts the digits. Others: 370, 371, 407, and 9474 with 4 digits.

Factorial and Fibonacci

n = 5
f = 1
for i in range(1, n + 1):
    f *= i
print("5! =", f)
a, b = 0, 1
for i in range(8):
    print(a, end=" ")
    a, b = b, a + b
print()

A product starts at 1, not 0. Fibonacci keeps the last two numbers; a, b = b, a + b moves both forward in one step.

Is it prime?

n = 91
is_prime = n >= 2
d = 2
while d * d <= n:
    if n % d == 0:
        is_prime = False
        break
    d += 1
print(n, "prime" if is_prime else "not prime")

A flag starts as "yes, prime" and flips on the first divisor. You only need to try divisors up to the square root (d * d <= n): if 91 = 7 × 13, the small factor 7 shows up first. 0 and 1 are not prime.

GCD by Euclid's method, then LCM

x, y = 12, 18
a, b = x, y
while b != 0:
    a, b = b, a % b
print("GCD:", a)
print("LCM:", x * y // a)

Replace (a, b) with (b, a % b) until b is 0; then a is the GCD. (12, 18) → (18, 12) → (12, 6) → (6, 0), so the GCD is 6. LCM = x × y ÷ GCD = 36.

Test the edges, where off-by-one bugs hide: 0! is 1; 1 is not prime; 2 is prime; a one-digit number is a palindrome. Also: a loop that eats n (like n //= 10) leaves n as 0, so keep a copy if you need the original.

These six are fixtures in CBSE Class 11 practicals and first-year lab exams, and placement tests (TCS NQT, Infosys) ask them as warm-up coding questions. Know each by heart as an idea, not as memorised lines: digits with % 10 / // 10, a flag for prime, a product starting at 1.

In one line

n % 10 is the last digit and n // 10 drops it; a product starts at 1, a prime check needs a flag or a loop else, and you should always test 0, 1 and 2.