欧博官网Factors of 120: Complete List, Prime Factoriza

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What are the Factor Pairs of 120?

The concept of factors of 120 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Learning how to find factors of 120 quickly builds number sense, helps in LCM/HCF questions, and improves calculation speed for competitive exams and school assessments.

What Are Factors of 120?

A factor of 120 is a whole number that divides 120 exactly, leaving no remainder. In other words, if you multiply two whole numbers and get 120, both those numbers are factors. This is useful for understanding composite numbers, finding common factors, and solving arithmetic or algebraic problems involving divisibility.

Complete List: The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Key Formula for Factors of 120

Here’s the standard formula using prime factors: $ 120 = 2^3 × 3^1 × 5^1 $
All factors can be generated by taking all possible products of powers of 2 (0 to 3), 3 (0 to 1), and 5 (0 to 1).

Prime Factorization of 120

Prime factors of 120 are the building blocks for the number. Breaking 120 into only prime number multipliers lets us see its structure clearly.

Divide 120 by 2: 120 ÷ 2 = 60

60 ÷ 2 = 30

30 ÷ 2 = 15

15 ÷ 3 = 5

5 ÷ 5 = 1

So, the prime factors of 120 are 2 × 2 × 2 × 3 × 5 or more compactly, 23 × 3 × 5.

Factor Pairs of 120

A factor pair of 120 consists of two whole numbers whose product is 120. For MCQs and mental maths, pair listing helps avoid missing factors.

Factor 1 Factor 2 Check
1 120 1 × 120 = 120
2 60 2 × 60 = 120
3 40 3 × 40 = 120
4 30 4 × 30 = 120
5 24 5 × 24 = 120
6 20 6 × 20 = 120
8 15 8 × 15 = 120
10 12 10 × 12 = 120

How to Find Factors of 120 (Stepwise Method)

Start with 1 and 120 (since 1 × 120 = 120)

Test every number from 2 up to the square root of 120 (about 10.95).

For each number n, if 120 ÷ n is whole, then n and 120÷n are both factors.

List these as factor pairs to avoid duplication and ensure you do not miss any.

For practice, follow the same method with another number, like the factors of 60.

Properties and Types of Factors of 120

Even factors: 2, 4, 6, 8, 10, 12, 20, 24, 30, 40, 60, 120
Odd factors: 1, 3, 5, 15
Prime factors: 2, 3, 5
Composite factors: 4, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Universal factors: 1 and 120 (the smallest and largest possible factors of 120).

Remember, all factors (except 1 and 120) are composite, since 120 is a composite number. For more on prime factors and composite numbers, check out those pages for definitions and examples.

Prime Factorization Tree of 120

Using a factor tree, you can visualize the prime decomposition:

120 breaks into 2 × 60

60 breaks into 2 × 30

30 breaks into 2 × 15

15 breaks into 3 × 5 (both prime)

So the full breakdown is 2 × 2 × 2 × 3 × 5. This tree method is especially useful in factorization and LCM/HCF questions.

Speed Trick or Vedic Shortcut

Here's a fast way to find factors of any number like 120: List 1 and the number, then keep checking consecutive numbers (2, 3, 4...) up to the square root, pairing each with its complement. For timed exams, write pairs vertically to avoid repeats!

Example: Check if 7 divides 120: 120 ÷ 7 = 17.14 (not a whole number, so 7 is not a factor). If the division gives a decimal, skip to the next. This trick works for all numbers.

Try These Yourself
Solved Examples

Example 1: Which pair of factors of 120 add up to 23?
1. List factor pairs: (1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), (10,12)

2. Check which sum is 23: 8 + 15 = 23
Final Answer: (8,15) is the pair.

Example 2: What is the highest common factor (HCF) of 90 and 120?
1. Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

2. Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

3. Common: 1, 2, 3, 5, 6, 10, 15, 30

4. HCF = 30

Example 3: What are the prime factors of 120?
120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5

Frequent Errors and Misunderstandings

Missing factor pairs by stopping at 10 (must check all up to square root of 120).

Confusing factors and multiples—remember, factors divide 120, while multiples are products like 240, 360, etc.

Ignoring 1 and 120 (always include smallest and largest for completeness).

Relation to Other Concepts

The idea of factors of 120 connects with LCM and HCF, multiplication tables, and the table of 20. Mastering factors supports algebra and number theory in higher classes, and also helps in daily logical reasoning.

Classroom Tip

To quickly find all factors of 120, list pairs systematically: Start with 1, then try 2, 3, 4 ..., checking for no remainder. Vedantu’s teachers use visual tables and short tricks in live classes to encourage stepwise, error-free thinking.

We explored factors of 120—from basics, listing, prime factorization, tricks, to connections with LCM and practice examples. Continue learning and practicing with Vedantu to build confidence in math and ace competitive exams!

Useful Internal Links

FAQs on Factors of 120: Definition, Prime Factors & Pairs

1. What are the factors of 120?

The factors of 120 are all whole numbers that can be multiplied in pairs to get 120. These factors include:

120

These numbers divide 120 without leaving any remainder, which makes them its exact divisors. Understanding factors is fundamental in topics like prime factorization and common divisors, which are frequently studied in Vedantu’s math curriculum.

2. What is the factor tree for 120?

A factor tree visually breaks down 120 into its prime factors. Starting with 120, you can split it as follows:

120

Divide by 2: 120 = 2 × 60

60 = 2 × 30

30 = 2 × 15

15 = 3 × 5

So, the prime factorization is $120 = 2^3 \times 3 \times 5$. Vedantu’s interactive lessons often use factor trees to help students build a strong foundation in prime factorization.

3. What are the multiples of 120?

Multiples of 120 are the numbers you obtain by multiplying 120 by whole numbers. Some of the first few multiples are:

120 × 1 = 120

120 × 2 = 240

120 × 3 = 360

120 × 4 = 480

120 × 5 = 600

In general, any number that can be expressed as $120 \times n$ (where $n$ is a whole number) is a multiple of 120. Practicing multiples helps students in areas like LCM and HCF, a key part of Vedantu’s math tutoring.

4. What makes 120 in Times Tables?

To find what makes 120 in times tables, look for pairs of numbers whose product is 120. Examples from multiplication tables are:

1 × 120

2 × 60

3 × 40

4 × 30

5 × 24

6 × 20

8 × 15

10 × 12

Each pair shows two numbers on multiplication tables that produce 120. Vedantu’s resources help reinforce this concept with interactive table practice.

5. How do you find the prime factors of 120?

To determine the prime factors of 120, divide it by the smallest prime numbers until only prime numbers remain. The steps are:

Divide by 2: 120 ÷ 2 = 60

60 ÷ 2 = 30

30 ÷ 2 = 15

15 ÷ 3 = 5

5 is a prime number

Thus, the prime factorization is $120 = 2^3 \times 3 \times 5$. Learning prime factorization is an essential part of mathematics covered in depth through Vedantu’s live classes.

6. What are the common factors of 120 and 96?

To find the common factors of 120 and 96, list the factors of each number and identify those they share:

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

The common factors are: 1, 2, 3, 4, 6, 8, 12, 24. Identifying common factors is a frequent topic in Vedantu’s math lessons for foundational skills.

7. Is 120 a composite number or a prime number?

120 is a composite number, not a prime number. This is because it has more than two distinct factors. Composite numbers have factors other than 1 and themselves.

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Vedantu’s courses explain how to recognize composites and primes to strengthen problem-solving skills.

8. What is the greatest common factor (GCF) of 120 and 180?

The greatest common factor (GCF) of 120 and 180 is the largest number that divides both exactly.

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

Their GCF is 60. Learning to find GCF is part of Vedantu’s math enrichment programs for students preparing for higher-level concepts.

9. How is 120 used in divisibility rules and tests?

The number 120 is often used in divisibility tests due to its many factors. Since it is divisible by 2, 3, 4, 5, 6, 8, 10, and 12, it serves as an excellent example when teaching divisibility rules. These properties help students quickly check which numbers can divide 120 without a remainder, a key skill learned via Vedantu’s conceptual videos and assignments.

10. What are some real-life applications involving the factors of 120?

Understanding the factors of 120 has many real-world uses such as:

Organizing objects into equal groups (like 120 pens in packets of 10, 12, or 15)

Scheduling tasks or dividing resources evenly

Simplifying fractions and ratios involving 120

Finding the number of possible rectangular arrangements (pairs of factors give possible lengths and widths)

Vedantu’s practical math sessions help students connect factors to everyday problem-solving.

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欧博官网Factors of 120: Complete List, Prime Factoriza

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