Answer:
The five numbers that have 12 factors are 96 , 90 , 84 , 72 , 60
Step-by-step explanation:
* Lets explain how to solve the problems
- The factors of 6 are 1 , 2 , 3 , 6 ⇒ 4 factors
- The factors of 12 are 1 , 2 , 3 , 4 , 6 , 12 ⇒ 6 factors
- We need a number with 12 factors twice the number of factors of 12
∴ We look for a multiple of 12 less than 100
- Lets start with 96 the greatest multiple of 12 and less than 100
∵ The factors of 96 are:
# 1 × 96
# 2 × 48
# 3 × 32
# 4 × 24
# 6 × 16
# 8 × 12
∴ 96 has 12 factors
∵ 84 is a multiple of 12
# 1 × 82
# 2 × 41
# 3 × 28
# 4 × 21
# 6 × 14
# 7 × 12
∴ 84 has 12 factors
∵ 72 is a multiple of 12
# 1 × 72
# 2 × 36
# 3 × 24
# 4 × 18
# 6 × 12
# 8 × 9
∴ 72 has 12 factors
∵ 60 is a multiple of 12
# 1 × 60
# 2 × 30
# 3 × 20
# 4 × 15
# 5 × 12
# 6 × 10
∴ 60 has 12 factors
- Now we have four numbers any multiple of 12 less than 60 has
number of factors less than 12
- So lets look for a multiple of 6 and less than 100
- The greatest multiple of 6 and less than 100 is 96 but we took it
before so lets take 90
∵ 90 is a multiple of 6
# 1 × 90
# 2 × 45
# 3 × 30
# 5 × 18
# 6 × 15
# 9 × 10
∴ 90 has 12 factors
* The five numbers that have 12 factors are 96 , 90 , 84 , 72 , 60
