Explain the terms 'factors' and 'product' in multiplication. Also, verify if the product of two 2-digit numbers can be a 3-digit or a 4-digit number, and provide examples.

Here are the answers to all the questions on the page.

Question 1:
The state that includes the two numbers multiplied (factors) and their product is called a multiplication relationship. The numbers multiplied are the factors, and the result is the product.
The relationship is that the product is a multiple of each of its factors. This means the product can be divided evenly by each of its factors.

Question 2:
Mamata says that the product of two 2-digit numbers can be a 3-digit or a 4-digit number.
Let's check:
The smallest 2-digit number is 10.
The largest 2-digit number is 99.
The smallest possible product of two 2-digit numbers is $10 \times 10 = 100$, which is a 3-digit number.
The largest possible product of two 2-digit numbers is $99 \times 99 = 9801$, which is a 4-digit number.
Therefore, Mamata's statement is ✅ Correct.

Question 3:
Mamata's statement is ✅ Correct.
Examples for two 2-digit numbers:

• For a 3-digit product:

$$10 \times 10 = 100$$ $$12 \times 15 = 180$$

• For a 4-digit product:

$$25 \times 40 = 1000$$ $$99 \times 99 = 9801$$

Question 4:
If a 2-digit number is multiplied by a 3-digit number, let's find the range of the product.
Smallest 2-digit number: 10
Largest 2-digit number: 99
Smallest 3-digit number: 100
Largest 3-digit number: 999
Smallest possible product: $10 \times 100 = 1000$ (a 4-digit number)
Largest possible product: $9