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Fractions practice

Prime factor trees

Break composite numbers into factor pairs until every branch ends in a prime, retaining repeated factors.

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Complete each factor split so that its two branches multiply to the parent number. Continue splitting composite leaves until every leaf is prime, then write their product as the prime factorization.

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US Letter

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A4

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Learning objective

What this activity builds

Represent a whole number as a product of primes and check that the completed tree preserves its value.

Worked example

Complete a factor tree for 36 beginning with 36 = 2 × 18.

36 = 2 × 2 × 3 × 3 = 2² × 3².

Split 18 into 2 × 9 and then 9 into 3 × 3. The leaves are 2, 2, 3 and 3. A different first split can lead to the same prime factors in a different order.

Teaching notes

Make the practice count

  • Check each parent-child multiplication before continuing down the tree.
  • Circle prime leaves and keep composite leaves available for further splitting.
  • Compare two trees for the same number to distinguish the tree arrangement from the unique prime-factor product.

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Math SheetNameScoreTeacherDate/ 22Prime Factor TreesComplete each factor tree and write the prime factorization.1.875Prime factors:2.210Prime factors:3.36Prime factors:4.98Prime factors:5.24Prime factors:6.28Prime factors:math-sheet.comPage 1 / 1

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