Factors of 252
The factors of 252 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 252) or (-1, -252), and are always integers, never fractions or decimals. You can find them using methods such as division or prime factorization. Learning about factors helps build a foundation for understanding divisibility, multiples, and prime numbers. In this guide, we'll explore the different types of factors of 252, including all positive factors, factor pairs, and the prime factorization of 252 with step-by-step explanations and examples.
What are the Factors of 252?
There are 18 factors of 252. The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126 and 252. Factors can be negative. The negative factors are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -63, -84, -126 and -252. All of these numbers divides 252 completely. 252 is a composite number because it has other factors besides 1 and 252.
Factors of 252: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126 and 252
Factor Pairs of 252
The factor pairs of 252 are the pairs of integers that multiply together to give 252. These include both positive and negative combinations. The positive factor pairs of 252 are (1, 252), (2, 126), (3, 84), (4, 63), (6, 42), (7, 36), (9, 28), (12, 21), (14, 18), and the negative factor pairs are (-1, -252), (-2, -126), (-3, -84), (-4, -63), (-6, -42), (-7, -36), (-9, -28), (-12, -21), (-14, -18). Knowing the factor pairs of 252 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 252:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 252 |
| 2 | 126 |
| 3 | 84 |
| 4 | 63 |
| 6 | 42 |
| 7 | 36 |
| 9 | 28 |
| 12 | 21 |
| 14 | 18 |
Negative Factor Pairs of 252:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -252 |
| -2 | -126 |
| -3 | -84 |
| -4 | -63 |
| -6 | -42 |
| -7 | -36 |
| -9 | -28 |
| -12 | -21 |
| -14 | -18 |
Prime Factorization of 252
The prime factorization of 252 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 252 are 2, 2, 3, 3, 7. Therefore, the prime factorization of 252 is 2^2 × 3^2 × 7. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 252:
2, 2, 3, 3, 7
Prime factorization of 252:
2 × 2 × 3 × 3 × 7
Compact form:
22 × 32 × 7
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How to Find the Factors of 252?
To find the factors of 252 using the division method efficiently, you only need to check numbers up to the square root of 252. For every number that divides 252 evenly, both it and its corresponding pair (252 ÷ that number) are factors.
Optimized steps to find factors of 252:
- •252 ÷ 1 = 252 → ✅ Factor Pair: (1, 252)
- •252 ÷ 2 = 126 → ✅ Factor Pair: (2, 126)
- •252 ÷ 3 = 84 → ✅ Factor Pair: (3, 84)
- •252 ÷ 4 = 63 → ✅ Factor Pair: (4, 63)
- •252 ÷ 6 = 42 → ✅ Factor Pair: (6, 42)
- •252 ÷ 7 = 36 → ✅ Factor Pair: (7, 36)
- •252 ÷ 9 = 28 → ✅ Factor Pair: (9, 28)
- •252 ÷ 12 = 21 → ✅ Factor Pair: (12, 21)
- •252 ÷ 14 = 18 → ✅ Factor Pair: (14, 18)
This method avoids unnecessary checks and gives all factor pairs quickly. It's especially useful for larger numbers.
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Frequently Asked Questions about factors of 252
What are the factors of 252?
The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
What is the prime factorization of 252?
The prime factorization of 252 is 2 × 2 × 3 × 3 × 7.
How do I find the factors of 252?
To find the factors of 252, start by dividing 252 by every number from 1 up to the square root of 252.
What are factor pairs of 252?
The factor pairs of 252 are (1, 252), (-1, -252), (2, 126), (-2, -126), (3, 84), (-3, -84), (4, 63), (-4, -63), (6, 42), (-6, -42), (7, 36), (-7, -36), (9, 28), (-9, -28), (12, 21), (-12, -21), (14, 18), (-14, -18).
How can I use the factors of 252?
The factors of 252 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 252 always positive?
Factors can be both positive and negative. For example, the negative factors of 252 are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -63, -84, -126, -252.