Which are the factor pairs of 22? 1, 22 2, 11 3, 19 4, 6 5, 17
The correct answer and explanation is:
The correct factor pairs of 22 are 1 and 22, and 2 and 11.
Explanation:
A factor pair of a number consists of two integers that, when multiplied together, equal that number. To find the factor pairs of 22, we look for all pairs of numbers such that:
a×b=22a \times b = 22
Now, let’s check the pairs provided:
- 1 and 22:
1×22=221 \times 22 = 22
This is true, so (1, 22) is a factor pair. - 2 and 11:
2×11=222 \times 11 = 22
This is true, so (2, 11) is a factor pair. - 3 and 19:
3×19=573 \times 19 = 57
This is false since 57 is not equal to 22. - 4 and 6:
4×6=244 \times 6 = 24
This is false since 24 is not equal to 22. - 5 and 17:
5×17=855 \times 17 = 85
This is false since 85 is not equal to 22.
Summary of factors of 22:
- 22 is a composite number, meaning it has factors other than 1 and itself.
- The factors of 22 are: 1, 2, 11, 22.
- The factor pairs combine these factors to produce the product 22:
- (1, 22)
- (2, 11)
No other pairs multiply exactly to 22, which means the only factor pairs of 22 are (1, 22) and (2, 11).
Additional note:
Since 22 is a product of two prime numbers (2 and 11), it has exactly two distinct prime factors. Factor pairs help in understanding divisibility and are useful in simplifying fractions, finding greatest common divisors (GCD), and solving various number theory problems.
If you want, I can also help you find factor pairs for other numbers or explain prime factorization in more detail!