Two numbers have a product of 4107, and their highest common factor (HCF) is 37. What is the larger of these two numbers?

Explanation

Let the two numbers be 37a and 37b, since their HCF is 37. Their product is given as 4107, so (37a) × (37b) = 4107, which simplifies to 37² × ab = 4107. Dividing both sides by 37² (which is 1369), we get ab = 3. The pairs of co-prime numbers with product 3 are (1, 3). Therefore, the numbers are 37 × 1 = 37 and 37 × 3 = 111. The larger number is 111.