Uvero — STEM Learning

Prime Factor Trees

A factor tree repeatedly splits a composite number until every leaf is prime. Different valid trees end with the same prime factors apart from order. A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

Split 60 into factors and continue until all factors are prime.
$60=2\times2\times3\times5=2^2\times3\times5$ .

Which is the prime factorisation of 60?

$2^2\times3\times5$

$2\times30$

$6\times10$

$3\times20$

Which statement best captures the central mathematical idea in Prime Factor Trees?

Different valid trees end with the same prime factors apart from order.

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Prime Factor Trees, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for prime factor trees.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Prime Factor Trees?

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

Different valid trees end with the same prime factors apart from order.

Represent the given information clearly and identify the operation or relationship required for prime factor trees.

Estimate first, then reverse the operation or use a second representation to check that the answer is reasonable.