529 = 23 × 23 = 23² — making it a perfect square. The only prime factor of 529 is 23, and the square root of 529 is 23.
529 is a perfect square AND the square of a prime number (23). Numbers that are squares of primes (like 4=2², 9=3², 25=5², 49=7², 529=23²) have exactly 3 factors: 1, the prime, and the square itself.
To find the prime factorisation of 529, divide by prime numbers starting from the smallest:
Step 1: Is 529 divisible by 2? No (it's odd) Step 2: Is 529 divisible by 3? 5+2+9=16, not divisible by 3 Step 3: Is 529 divisible by 5? No (doesn't end in 0 or 5) Step 4: Is 529 divisible by 7? 529 ÷ 7 = 75.57... No Step 5: Is 529 divisible by 11? 529 ÷ 11 = 48.09... No Step 6: Is 529 divisible by 13? 529 ÷ 13 = 40.69... No Step 7: Is 529 divisible by 17? 529 ÷ 17 = 31.11... No Step 8: Is 529 divisible by 19? 529 ÷ 19 = 27.84... No Step 9: Is 529 divisible by 23? 529 ÷ 23 = 23 ✓
529 = 23 × 23 = 23²
(We only need to check primes up to √529 ≈ 23)
529
|
23 × 23
529 has only one unique prime factor: 23
Since 529 = 23², it is a perfect square. √529 = 23
Verification: 23 × 23 = (20+3)(20+3) = 400 + 60 + 60 + 9 = 529 ✓
Neighbouring perfect squares:
529 has only 3 factors: **1, 23, and 529**. This is because 529 = 23² — a square of a prime always has exactly 3 factors.
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