If the HCF of two numbers is 5 and their product is 100, what could be the two n

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Question: If the HCF of two numbers is 5 and their product is 100, what could be the two numbers? (2023)

Options:

Correct Answer: 5 and 20

Exam Year: 2023

Solution:

If HCF is 5, the two numbers can be expressed as 5a and 5b. Thus, 5a * 5b = 100 implies ab = 4. The pair (1, 4) gives us 5 and 20.

If the HCF of two numbers is 5 and their product is 100, what could be the two numbers? (2023)

If the HCF of two numbers is 5 and their product is 100, what could be the two numbers? (2023)

Step 1: Understand that the HCF (Highest Common Factor) of the two numbers is 5.
Step 2: Since the HCF is 5, we can express the two numbers as 5a and 5b, where a and b are whole numbers.
Step 3: The product of the two numbers is given as 100. So, we can write the equation: (5a) * (5b) = 100.
Step 4: Simplify the equation: 25ab = 100.
Step 5: Divide both sides of the equation by 25 to find ab: ab = 100 / 25 = 4.
Step 6: Now, we need to find pairs of whole numbers (a, b) that multiply to give 4.
Step 7: The pairs of whole numbers that multiply to 4 are (1, 4) and (2, 2).
Step 8: Substitute these pairs back to find the original numbers: For (1, 4), we get 5*1 = 5 and 5*4 = 20. For (2, 2), we get 5*2 = 10 and 5*2 = 10.
Step 9: Therefore, the possible pairs of numbers are (5, 20) and (10, 10).

Highest Common Factor (HCF) – Understanding the concept of HCF and how it relates to the factors of numbers.
Product of Numbers – Using the relationship between the product of two numbers and their HCF to derive possible values.
Factorization – Breaking down numbers into their factors to find pairs that meet given conditions.