Unit 3 · Topic 04 · Playing with Numbers
Ms. Rao wrote 60 on the board and asked for its "prime building blocks" — the smallest prime numbers that multiply together to make it.
Kabir drew branches splitting 60 into smaller and smaller pieces, like a family tree. Anaya divided 60 by primes one after another, straight down a column.
Two completely different-looking methods — and they landed on the exact same four numbers.
"Every whole number bigger than 1 is either prime itself, or can be broken down into a unique set of prime numbers multiplied together," said Ms. Rao. "Let's find the primes hiding inside 60, two different ways."
Kabir tried the FACTOR TREE. He split 60 into 6 x 10. Neither 6 nor 10 is prime, so he split again: 6 became 2 x 3, and 10 became 2 x 5. Now every branch ended in a prime — 2, 3, 2, 5. "So 60 = 2 x 3 x 2 x 5," he said, rearranging to 2 x 2 x 3 x 5.
Anaya tried the DIVISION METHOD. She divided 60 by the smallest prime that fit: 60 / 2 = 30. Then 30 / 2 = 15. Since 15 isn't divisible by 2, she moved to the next prime: 15 / 3 = 5. Since 5 is already prime, she divided by 5: 5 / 5 = 1 and stopped. Reading the divisors down: 2, 2, 3, 5.
"Same four primes, same order once arranged: 2 x 2 x 3 x 5," said Ms. Rao. "The tree branches out; the division method goes straight down a column. Different pictures, same underlying answer — because every number's prime factorisation is unique, no matter which path you take to find it."
Prime factorisation breaks a number down into the prime numbers that multiply together to make it.
The Factor Tree method: split the number into any two factors, then keep splitting any non-prime factor further, until every branch ends in a prime.
The Division method: repeatedly divide the number by the smallest prime that divides it exactly, writing down each prime divisor, until the result reaches 1.
Both methods always give the same set of prime factors for a given number — this is called the uniqueness of prime factorisation.
Find the prime factorisation of 72 using the factor tree method.
Find the prime factorisation of 72 using the division method, and check both answers match.
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