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Factors of 28 – Definition With Examples

Jo-ann Caballes

Updated on September 30, 2026

The factors of 28 are 1, 2, 4, 7, 14, and 28 — the whole numbers that divide 28 with nothing left over. Every one of these numbers multiplies with another factor on the list to make exactly 28, which is why they’re often shown in matching pairs. This guide covers 28’s factor pairs, its prime factorization, and a few of its more unusual properties — solid grounding for students working with elementary math tutors on multiplication and division.

What Are the Factors of 28?

Factors of 28 are any whole numbers that divide 28 without leaving a remainder — in other words, two numbers that multiply together to make 28. Every number has at least two factors, 1 and itself, and 28 has six factors in total:

• 1
• 2
• 4
• 7
• 14
• 28

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Factor Pairs of 28

In a factor pair, two numbers multiply together to make 28. The factor pairs of 28 are 1 × 28, 2 × 14, and 4 × 7.

Every positive factor pair has a matching negative pair too, since a negative times a negative also gives a positive result: (−1) × (−28) = 28, (−2) × (−14) = 28, and (−4) × (−7) = 28. Most school-level work with factors sticks to the positive pairs, but it’s worth knowing the negative versions exist.

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Properties of the Factors of 28

There are several ways to multiply back to 28 by combining its factors. These factor pairs can be used to share, organize, and solve basic math problems, like dividing 28 evenly:

Real-world uses for these factor pairs include:

• Dividing 28 apples evenly into baskets
• Designing a game board or path with 28 steps
• Arranging 28 books evenly across shelves

28 Is a Perfect Number

If you add up every factor of 28 except 28 itself — 1 + 2 + 4 + 7 + 14 — the total is exactly 28. A number whose factors (other than itself) add up to the number is called a perfect number, and 28 is the second-smallest one (after 6). Perfect numbers are rare — the next one after 28 is 496.

Difference Between Factors of 28 and Multiples of 28

Factors and multiples describe opposite ideas: factors divide a number into smaller parts, while multiples grow it larger. The numbers 1, 2, 4, 7, 14, and 28 are factors of 28 because they divide it perfectly — these are the answer to “what numbers go into 28?”

Multiples of 28, on the other hand, are what you get by multiplying 28 by whole numbers: 28, 56, 84, 112, and so on, growing without limit.

How to Find the Factors of 28

To find a factor of 28, check which whole numbers divide it with nothing left over. A quick shortcut: you only need to test numbers up to the square root of 28 (about 5.3, so up to 5) — every factor above that point already has a matching partner below it, from the prime factorization of the number.

Steps to Find the Factors of 28

1. Start with 1 — 28 ÷ 1 = 28, so 1 and 28 are a factor pair.
2. Check 2 — 28 ÷ 2 = 14, so 2 and 14 are a factor pair.
3. Check 3 — 28 ÷ 3 leaves a remainder, so skip it.
4. Check 4 — 28 ÷ 4 = 7, so 4 and 7 are a factor pair.
5. Stop once you pass the square root of 28 (≈ 5.3) — every factor from here on has already been found as part of an earlier pair.

This gives all six factors: 1, 2, 4, 7, 14, and 28. From this list, the prime factorization of 28 is 2 × 2 × 7, or 2² × 7.

Practice Problems on Finding Factors of 28

• List all the factors of 28 and arrange them from smallest to largest.
• Write the factors of 28 in pairs.
• Distribute 28 candies evenly among 7 friends. How many candies does each friend receive?
• Use the prime factorization of 28 to show it can be built by multiplying smaller numbers together.

Answer Key

• 1, 2, 4, 7, 14, 28
• 1 × 28, 2 × 14, 4 × 7
• 28 ÷ 7 = 4 candies each
• 28 = 2 × 2 × 7 (2² × 7)

Factors of 28 Worksheets

Put this into practice with related Brighterly worksheets:

• Factor tree worksheets
• Greatest common factor worksheets
• Factors and multiples worksheets
• Prime and composite numbers worksheets

Frequently Asked Questions on Factors of 28

What Are Factors of 28?

Factors of 28 are numbers that divide 28 exactly, with nothing left over. You can split 28 into equal groups using any of them without a remainder.

What Are All the Factors of 28?

All the factors of 28 are 1, 2, 4, 7, 14, and 28 — six factors in total, forming the three factor pairs 1 × 28, 2 × 14, and 4 × 7.

What Is the Prime Factorization of 28?

The prime factorization of 28 shows which prime numbers multiply together to make it. For 28, that’s 2 × 2 × 7, or 2² × 7, since 2 and 7 are both prime numbers.

Is 28 a Prime Number?

No, 28 isn’t a prime number. It has more than two factors — 1, 2, 4, 7, 14, and 28 — which means it can be broken into smaller whole-number parts, unlike a prime number, which only has 1 and itself as factors.

Is 28 a Perfect Number?

Yes. Adding up all of 28’s factors except itself — 1 + 2 + 4 + 7 + 14 — equals exactly 28, which is the definition of a perfect number. It’s the second perfect number, after 6.

What’s the Difference Between Factors and Multiples of 28?

Factors of 28 (1, 2, 4, 7, 14, 28) divide evenly into it, while multiples of 28 (28, 56, 84, 112, …) are what you get by multiplying 28 by whole numbers. Factors break a number down; multiples build it up.

Jo-ann Caballes

29 articles

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.