Factors of 147
Every number has factors, and the factors of 147 are the ones that divide it exactly, leaving no remainder. They include both positive and negative numbers and always come in pairs, one small, one large. You can find the factors of 147 by dividing it by smaller numbers or using prime factorization. Learning about factors helps in many math topics, such as divisibility, multiples, and greatest common factors. Below, we’ll explore the complete list of factors of 147, all factor pairs, and the prime factorization with step-by-step explanations.
What are the Factors of 147?
The factors of 147 are the numbers that can divide it exactly with no remainder left behind. Those numbers are 1, 3, 7, 21, 49 and 147. Their negative counterparts are -1, -3, -7, -21, -49 and -147. Each factor contributes to the mathematical makeup of 147. Knowing factors helps you understand multiplication, division, and number properties. 147 is a composite number because it can be expressed as a product of smaller integers.
Factors of 147: 1, 3, 7, 21, 49 and 147
Factor Pairs of 147
The factor pairs of 147 represent all the ways two numbers can multiply to result in 147. The positive pairs are (1, 147), (3, 49), (7, 21), and the negative ones are (-1, -147), (-3, -49), (-7, -21). Each pair is a mirror of how numbers work together in multiplication. Learning about factor pairs strengthens your understanding of multiplication, division, and number patterns, and connects to topics like the greatest common factor and prime numbers. You can also explore how factor pairs relate to the greatest common factor and prime factorization for deeper understanding.
Positive Factor Pairs of 147:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 147 |
| 3 | 49 |
| 7 | 21 |
Negative Factor Pairs of 147:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -147 |
| -3 | -49 |
| -7 | -21 |
Prime Factorization of 147
Prime factorization means expressing a number as a multiplication of its prime numbers. For the number 147, the prime factors obtained through repeated division are 3, 7, 7. Hence, the prime factorization of 147 is 3 × 7^2. This knowledge is widely used in various areas of mathematics, including finding LCM, GCF, and reducing fractions to their simplest form.
Prime factors of 147:
3, 7, 7
Prime factorization of 147:
3 × 7 × 7
Compact form:
3 × 72
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How to Find the Factors of 147?
To explore the factors of 147, start by dividing it by integers up to its square root. Each number that divides 147 completely forms a factor pair with the quotient, giving both members of the pair. This method minimizes redundant checks and provides a clear way to see how 147 can be expressed as products of smaller numbers. It’s particularly useful for students learning divisibility, multiplication, and the basics of number theory.
Optimized steps to find factors of 147:
- •147 ÷ 1 = 147 → ✅ Factor Pair: (1, 147)
- •147 ÷ 3 = 49 → ✅ Factor Pair: (3, 49)
- •147 ÷ 7 = 21 → ✅ Factor Pair: (7, 21)
This method avoids unnecessary checks and quickly identifies all factor pairs, making it especially helpful for larger numbers.
Find factors and factor pairs of any number with our Factor Checker tool.
Frequently Asked Questions about factors of 147
What are the factors of 147?
The factors of 147 are 1, 3, 7, 21, 49, 147.
What is the prime factorization of 147?
The prime factorization of 147 is 3 × 7 × 7.
How do I find the factors of 147?
To find the factors of 147, start by dividing 147 by every number from 1 up to the square root of 147.
What are factor pairs of 147?
The factor pairs of 147 are (1, 147), (-1, -147), (3, 49), (-3, -49), (7, 21), (-7, -21).
How can I use the factors of 147?
The factors of 147 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 147 always positive?
Factors can be both positive and negative. For example, the negative factors of 147 are -1, -3, -7, -21, -49, -147.