Solution:

Using a factor tree: $18 = 2 \times 9$ $9 = 3 \times 3$

So: $18 = 2 \times 3 \times 3 = 2 \times 3^2$

Answer: $18 = 2 \times 3^2$

Solution:

Using a factor tree: $18 = 2 \times 9$ $9 = 3 \times 3$

So: $18 = 2 \times 3 \times 3 = 2 \times 3^2$

Answer: $18 = 2 \times 3^2$

Solution:

Check if any prime numbers less than 37 divide it evenly:

• $37 \div 2 = 18.5$ (not whole)
• $37 \div 3 = 12.33...$ (not whole)
• $37 \div 5 = 7.4$ (not whole)
• We only need to check up to $\sqrt{37} \approx 6$

Since no prime numbers divide 37 evenly, it has no factors other than 1 and 37.

Answer: 37 is a prime number

Solution:

Check if any prime numbers less than 37 divide it evenly:

• $37 \div 2 = 18.5$ (not whole)
• $37 \div 3 = 12.33...$ (not whole)
• $37 \div 5 = 7.4$ (not whole)
• We only need to check up to $\sqrt{37} \approx 6$

Since no prime numbers divide 37 evenly, it has no factors other than 1 and 37.

Answer: 37 is a prime number

Solution:

Using the division method: $180 \div 2 = 90$ $90 \div 2 = 45$ $45 \div 3 = 15$ $15 \div 3 = 5$ $5 \div 5 = 1$

So: $180 = 2 \times 2 \times 3 \times 3 \times 5 = 2^2 \times 3^2 \times 5$

Answer: $180 = 2^2 \times 3^2 \times 5$

Solution:

Using the division method: $180 \div 2 = 90$ $90 \div 2 = 45$ $45 \div 3 = 15$ $15 \div 3 = 5$ $5 \div 5 = 1$

So: $180 = 2 \times 2 \times 3 \times 3 \times 5 = 2^2 \times 3^2 \times 5$

Answer: $180 = 2^2 \times 3^2 \times 5$