How many ways can 840 be written as the product of two numbers ?
2025
How many ways can 840 be written as the product of two numbers ?
- A.
32
- B.
16
- C.
6
- D.
18
Attempted by 16 students.
Show answer & explanation
Correct answer: B
Answer: 16 ways
Prime factorization: 840 = 2^3 × 3 × 5 × 7
Number of positive divisors = (3+1)(1+1)(1+1)(1+1) = 4 × 2 × 2 × 2 = 32.
Each divisor d pairs with 840/d to make a product of 840. Counting unordered pairs (where a·b and b·a are the same) means we divide the divisor count by 2: 32 ÷ 2 = 16.
Note: Because 840 is not a perfect square, there is no divisor equal to its own pair, so dividing by 2 gives the correct count of unordered pairs.
Therefore, there are 16 ways to write 840 as the product of two positive integers when order does not matter.