🧮 Prime Factorisation Trainer

Break any number into its prime factors with a full working ladder, learn the divisibility rules, then practise finding the next prime factor yourself. Primes are the building blocks of every whole number — this tool shows you why. Runs on your device.

Factor a number (2 – 2000)
Practice — divide step by step
— Find the next prime factor:
Divisibility rules
• 2 — last digit is even (0,2,4,6,8)
• 3 — digit sum is divisible by 3 (360 → 3+6+0=9)
• 5 — last digit is 0 or 5
• 7 — double the last digit, subtract from the rest, repeat
• 11 — alternating sum of digits is 0 or a multiple of 11
• prime — a number whose only factors are 1 and itself
Why it matters
• The fundamental theorem of arithmetic: every whole number > 1 has one unique prime factorisation.
• Factorising is how we find HCF and LCM — track the highest/lowest powers shared.
• Cryptography relies on it: multiplying two large primes is easy, unpicking the product is extremely hard.
Primes under 200

Note: the ladder uses the smallest prime factor at each step — that produces the unique prime factorisation. 1 is neither prime nor composite.