What times what equals 98?
The Correct Answer and Explanation is:
To find out what two numbers multiply together to equal 98, we can start by identifying the factors of 98. A factor is a whole number that can be multiplied by another whole number to yield a given product.
Factors of 98
- Identifying Basic Factors:
The simplest method to find the factors of 98 is to start from 1 and go up to 98 itself. The first factor is always 1, since any number multiplied by 1 remains the same. Next, we check for the smallest whole numbers:
- 1 × 98 = 98
- 2 × 49 = 98 (since 98 is even, it is divisible by 2)
- 7 × 14 = 98 (dividing 98 by 7 gives us 14)
- Further Analysis:
So far, we have identified the pairs: (1, 98), (2, 49), and (7, 14). These pairs are the factors of 98, and they can be written as:
- (1, 98)
- (2, 49)
- (7, 14)
- Prime Factorization:
Another way to understand how we arrive at these factors is through prime factorization. We can break down 98 into its prime components:
- First, divide by 2: (98 ÷ 2 = 49)
- Then, break down 49, which is (7 × 7) or (7^2) Thus, the prime factorization of 98 is (2 × 7^2).
- Summary of Factors:
From the prime factorization, we see that the factors of 98 can be derived from the combinations of these primes. The complete list of pairs that can be multiplied to equal 98 is:
- (1, 98)
- (2, 49)
- (7, 14)
In conclusion, the pairs of numbers that multiply to equal 98 are (1 \times 98), (2 \times 49), and (7 \times 14). Each of these pairs demonstrates the multiplicative relationships that yield the product of 98, confirming that 98 has multiple pairs of factors.