How do you find all the factors and factor pairs of 28?
The concept of factors of 28 is fundamental in mathematics. Knowing the factors of 28 helps students solve exam questions, build their number sense, and apply maths in real-life sharing or grouping scenarios.
What Are Factors of 28?
A factor of 28 is any number that divides 28 evenly, leaving no remainder. In other words, when you multiply two such numbers together, you get 28 as the answer. Factors are always whole numbers. Common places you'll see factors of 28 are in LCM and HCF calculations, prime factorization, and real-life problems involving grouping or sharing.
List of All Factors of 28
The complete list of positive factors of 28 is: 1, 2, 4, 7, 14, 28. This means these numbers can divide 28 with no remainder. Each factor also pairs with another to make 28 when multiplied.
| Factor Pair | Multiplication |
|---|---|
| 1 and 28 | 1 × 28 = 28 |
| 2 and 14 | 2 × 14 = 28 |
| 4 and 7 | 4 × 7 = 28 |
How to Find All Factors of 28: Step-by-Step Guide
- Start by writing the number 28.
- Check every number from 1 up to 28 and see if it divides 28 exactly:
- If the division leaves no remainder, add both the divisor and quotient as factors.
- Continue up to the square root of 28 (about 5.29). If you reach a number whose square is more than 28, stop — all larger factor pairs will already be listed in reverse.
Prime Factorization of 28
The prime factorization of 28 breaks it down into just prime numbers. Let’s use the division method:
- Divide 28 by 2 (smallest prime): 28 ÷ 2 = 14.
- Divide 14 by 2: 14 ÷ 2 = 7.
- Now, 7 is a prime number, so you stop here.
So, the prime factors of 28 are 2 × 2 × 7 or \( 2^2 \times 7 \).
Factor Pairs of 28
A factor pair of 28 is any two whole numbers that, when multiplied, give 28. The positive factor pairs are:
- (1, 28)
- (2, 14)
- (4, 7)
Negative pairs are also possible by using the negative versions of each: (-1, -28), (-2, -14), (-4, -7).
Speed Trick (Divisibility Test)
To quickly find if a number is a factor of 28, check if it divides 28 with no remainder. For example, since 28 ends in 8 (an even number), 2 is always a factor of even numbers. Try dividing by small primes up to 7 to spot factors fast!
Real-Life Example
Suppose you have 28 candies and need to divide them equally among friends. You can only choose a group size that is a factor of 28 (such as 2, 4, 7, or 14), so no candy is left over!
Common Mistakes
- Thinking that decimals or negative numbers (other than pairs) are factors — only whole numbers count, and pairs should both be integers.
- Confusing factors with multiples. Factors of 28 are finite (only six positive), but multiples of 28 go on forever (like 28, 56, 84, 112...)
Relation to Other Number Concepts
Understanding the factors of 28 also helps with learning multiples, as well as LCM and HCF of numbers in higher classes. Factors make it easier to solve word problems and identify patterns in maths tables like those on multiplication tables.
Try These Yourself
- Find the factors of 24 and compare them with the factors of 28. (Use Factors of 24 page for help).
- Is 28 a composite number? Why?
- How many different factor pairs can you make with 28?
- Check if 32 is a factor of 28 (helpful link).
Classroom Tip
A fun way to remember the factors of 28 is to draw a “factor rainbow”—draw arcs from 1 to 28, 2 to 14, and 4 to 7. This visual cue makes it easy to recall “who pairs with whom” to make 28. Vedantu’s teachers often use such visual factor tricks in live classes!
We explored factors of 28—from their meaning, listing, pairs, prime factorization, and quick tricks. Keep practicing with examples or by comparing with numbers like 24 or 32. With practice and support from Vedantu, you’ll soon become an expert at factors and other maths tricks!
Explore Related Topics:
Factors of 24 |
Factors of 32 |
Prime Factors |
Factors of 30 |
Multiples
FAQs on Factors of 28 – Definition, List, Pairs & Prime Factorization
1. What are the factors of 28?
The factors of 28 are the whole numbers that divide 28 without leaving a remainder. These are: 1, 2, 4, 7, 14, and 28.
2. What are the factor pairs of 28?
Factor pairs are sets of two numbers that multiply to give 28. The pairs are: (1, 28), (2, 14), and (4, 7). Remember that (28, 1), (14, 2), and (7, 4) are also factor pairs, but these are simply the reverse of the ones already listed.
3. How many factors does 28 have?
The number 28 has six factors: 1, 2, 4, 7, 14, and 28.
4. What is the prime factorization of 28?
The prime factorization of 28 is 2 x 2 x 7, or 2² x 7. This means 28 can be expressed as a product of only prime numbers (numbers divisible only by 1 and themselves).
5. What is a factor tree for 28?
A factor tree visually represents the prime factorization. For 28, you would start with 28, then branch it into 2 and 14. The 2 is prime, so you stop there. The 14 branches into 2 and 7, both of which are prime. The final prime factors are 2, 2, and 7.
6. How do I find all the factors of a number?
To find all the factors of a number, systematically divide the number by each whole number, starting from 1, and check if the result is also a whole number. If it is, both the divisor and the quotient are factors. Repeat until the quotient becomes less than the divisor.
7. Is 28 a composite number?
Yes, 28 is a composite number because it has more than two factors (1 and itself).
8. What are the common factors of 28 and another number (e.g., 14)?
To find the common factors of 28 and another number, list the factors of each number and identify the numbers that appear in both lists. For example, the common factors of 28 and 14 are 1, 2, 7, and 14.
9. How are factors of 28 used in finding the Highest Common Factor (HCF)?
The HCF of two or more numbers is the largest number that divides all of them evenly. To find the HCF, list the factors of each number and find the largest number common to all lists. For example, to find the HCF of 28 and 14, list their factors and you'll find 14 is the HCF.
10. How are factors used in finding the Lowest Common Multiple (LCM)?
The LCM is the smallest number that is a multiple of two or more numbers. Factors are helpful in finding the LCM using methods like prime factorization. By identifying the prime factors, you can build the LCM by including the highest power of each prime factor present in the numbers.
11. Can factors of 28 include negative numbers?
While typically we focus on positive factors, it's true that -1, -2, -4, -7, -14, and -28 also divide 28 evenly. Therefore, negative numbers can be considered factors as well.
12. What is the difference between factors and multiples of 28?
Factors are numbers that divide 28 evenly, while multiples are numbers that result from multiplying 28 by another whole number. Factors are finite, while multiples are infinite. The factors of 28 are 1, 2, 4, 7, 14, and 28. Multiples of 28 include 28, 56, 84, 112, etc.
