Find from Factors
Weekly Problem 35 - 2006
A number has exactly eight factors, two of which are 21 and 35. What is the number?
A number has exactly eight factors, two of which are 21 and 35. What is the number?
Age
11 to 14
Challenge level
Problem
A certain number has exactly eight factors including $1$ and itself. Two of its factors are $21$ and $35$. What is the number?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 105
21 and 35 are factors
so 3, 7 and 5, 7 are prime factors
If 3, 5 and 7 are the only prime factors then the factors are:
1, 3, 5, 7,
15, 21, 35, and the number itself
The number itself = 3$\times$5$\times$7 = 105