2.2 Prime factorisation, HCF and LCM — Practise

1. Prime factors of 72

• $72$
• $2*36$
• $2*2*18$
• $2*2*2*9$
• $2^3*3^2$

Answer: $72=2^3\\times3^2$

2. Prime factors of 90

Answer: $90=2\\times3^2\\times5$

3. HCF of 24 and 40

Answer: $24=2^3\\times3$ and $40=2^3\\times5$, so the HCF is $2^3=8$.

4. LCM of 15 and 20

Answer: $15=3\\times5$ and $20=2^2\\times5$, so the LCM is $2^2\\times3\\times5=60$.

5. HCF of 36 and 60

Answer: $36=2^2\\times3^2$ and $60=2^2\\times3\\times5$, so HCF $=2^2\\times3=12$.

6. LCM of 8 and 18

Answer: $8=2^3$ and $18=2\\times3^2$, so LCM $=2^3\\times3^2=72$.

7. Identical sets

Answer: The HCF of 48 and 60 is 12, so she makes 12 sets, each with 4 pencils and 5 pens.

8. Lights flashing together

Answer: Use the LCM: $36$ seconds.

9. Prime factors and HCF

Answer: $150=2\\times3\\times5^2$ and $210=2\\times3\\times5\\times7$, so the HCF is $2\\times3\\times5=30$.