Long division and prime factors
Answers are for parents and teachers.
1
Divide 3,726 ÷ 18. Estimate first, then check with multiplication.
207. Estimate: 3,600 ÷ 18 = 200. Check: 18 × 207 = 3,726.
2
A school has 1,300 pupils and each classroom holds 35. How many classrooms are needed?
1,300 ÷ 35 = 37 remainder 5, so 38 classrooms (the 5 pupils need a room too).
3
Draw a factor tree for 54 and write 54 as a product of primes.
54 = 6 × 9 = 2 × 3 × 3 × 3. So 54 = 2 × 3 × 3 × 3 (any correct tree is fine).
4
Draw the Venn diagram of the primes of 18 and 30, then find the GCF and the LCM.
18 = 2 × 3 × 3 and 30 = 2 × 3 × 5. Overlap: 2 and 3, so GCF = 6. Only 18: 3. Only 30: 5. LCM = 2 × 3 × 3 × 5 = 90.
5
Show that 25 and 42 are relatively prime.
25 = 5 × 5 and 42 = 2 × 3 × 7. They have no prime in common, so their only common factor is 1.