Math · Stage 4
Use products, sums and prime factors to find numbers
Break a number into its prime building blocks, and use a product-and-sum clue to find two hidden numbers — the detective tricks of number olympiads.
✦ Math📘 Stage 4 · S4⏱ ~12 min🧒 Ages 8–9★ Free to start
I can use products, sums and prime factors to find numbers.
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Kavi the Number Detective 🔎
Kavi has two clues on the board. "Two secret numbers multiply to 12 and add to 7," whispers Kavi. "Every number is built from primes — find those blocks and the mystery numbers appear 🔎!"
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What your child will learn
1Prime or composite?A prime number has exactly two factors: 1 and itself — it cannot be split into a product of smaller numbers. A composite number can. Primes are the building blocks of every other number. Sort each one.
2Build a prime factor treeTo find a number's prime factors, keep splitting it into a product until every branch is prime. Start 24 two different ways — you always reach the same primes. Tap each card.
3Two clues: a product AND a sumA classic olympiad clue: two numbers multiply to 12 and add to 7. List the factor pairs of 12 — (1,12), (2,6), (3,4) — then check which pair adds to 7. Tap more ▶ and ◀ less to test sums that make 7.
4Which numbers have 7 as a factor?A number has 7 as a factor exactly when it appears in the 7 times table. The lit numbers are the multiples of 7: 7, 14, 21, 28, 35… — so 35 has 7 as a factor, but 30 does not.
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A peek inside
Find two numbers that multiply to 12 and add to 7.
factor pairs of 12: (1,12)→13, (2,6)→8, (3,4)→7 ✓
Try this at home: Product & sum: two numbers multiply to 10 and add to 7. They are __ and __
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 4 · S4 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.