What are the Factors and Factor Pairs of 150?
The concept of factors of 150 is important in Maths for fast calculations, prime factorization, finding common multiples, and solving HCF or LCM problems in exams or day-to-day scenarios.
What Are Factors of 150?
A factor of 150 is any whole number that divides 150 exactly with zero remainder. These numbers can be written as pairs, used in calculations, and are essential for many Maths applications such as finding HCF, LCM, and understanding divisibility. The full list of factors of 150 includes only positive whole numbers: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. Knowing these divisors helps solve word problems, quick MCQs, and more.
How to Find Factors of 150
To find the factors of 150, check which numbers divide 150 with no remainder. Here’s a step-by-step approach:
- Start from 1 and move upwards.
1 divides every integer, so 1 is a factor. - Try dividing by 2:
150 ÷ 2 = 75 (no remainder), so 2 is a factor. - Continue with 3, 4, 5, etc. until you reach 150.
3: 150 ÷ 3 = 50 → factor
4: 150 ÷ 4 = 37.5 → not a factor
5: 150 ÷ 5 = 30 → factor - Repeat for every number up to 150.
- List all whole divisors where 150 ÷ divisor leaves no remainder.
Shortcut: You only need to check up to the square root of 150 (around 12.25), since above that, factors repeat in pairs. Pair each factor found with 150 divided by that factor to get all pairs quickly.
All Factors of 150 in Pairs
Factor pairs are two numbers that multiply to give 150. Here is a complete list:
| Positive Pair | Calculation | Negative Pair |
|---|---|---|
| (1, 150) | 1 × 150 = 150 | (-1, -150) |
| (2, 75) | 2 × 75 = 150 | (-2, -75) |
| (3, 50) | 3 × 50 = 150 | (-3, -50) |
| (5, 30) | 5 × 30 = 150 | (-5, -30) |
| (6, 25) | 6 × 25 = 150 | (-6, -25) |
| (10, 15) | 10 × 15 = 150 | (-10, -15) |
So, the positive factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.
Prime Factorization of 150
The prime factors of 150 are found by dividing 150 by the smallest primes until you reach 1.
- Divide 150 by 2: 150 ÷ 2 = 75
- Divide 75 by 3: 75 ÷ 3 = 25
- Divide 25 by 5: 25 ÷ 5 = 5
- Divide 5 by 5: 5 ÷ 5 = 1
So, 150 = 2 × 3 × 5 × 5 = 2 × 3 × 52.
Prime Factorization Tree:
↓
2 × 75
↓
2 × 3 × 25
↓
2 × 3 × 5 × 5
This prime factorization is used in topics like HCF and LCM problems and quickly checking divisibility.
Properties and FAQs - Factors of 150
- 150 is a composite number (more than 2 factors).
- It is an even number, since 2 is a factor.
- The smallest factor is 1; the largest is 150 itself.
- The prime factors are 2, 3, and 5.
- 150 is not a perfect square, but 25 is a perfect square that is a factor of 150.
Frequently Asked Questions
Q1: What are the factors of 150?
A: The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
Q2: How many factors does 150 have?
A: There are 12 positive factors of 150.
Q3: What is the prime factorization of 150?
A: 150 = 2 × 3 × 5 × 5 = 2 × 3 × 52
Q4: Which factors of 150 are perfect squares?
A: 1 and 25 are perfect square factors.
Q5: Which are the factor pairs of 150?
A: (1,150), (2,75), (3,50), (5,30), (6,25), (10,15)
Practice Problems – Factors of 150
- Find all the factors of 150 that are also multiples of 5.
- List the common factors of 150 and 75.
- Is 12 a factor of 150?
- Write the sum of all factors of 150 (excluding 150).
- Identify which of these are factors of 150: 10, 13, 25, 48.
Stepwise Solutions:
1. Factors of 150 that are multiples of 5: 5, 10, 15, 25, 30, 50, 75, 1502. Common factors of 150 and 75:
75: 1, 3, 5, 15, 25, 75
Common: 1, 3, 5, 15, 25, 75
3. 12 is not a factor of 150, since 150 ÷ 12 = 12.5.
4. Sum (excluding 150): 1+2+3+5+6+10+15+25+30+50+75 = 222
5. Factors among 10, 13, 25, 48: Only 10 and 25 are factors.
Applications of Factors of 150
Factors of 150 are useful for:
- Finding HCF and LCM with numbers like 60 or 75.
- Simplifying fractions, like reducing 150/75 = 2.
- Divisibility checks in word problems or exams.
- Breaking down real-life situations: Packing in groups, arranging objects evenly, and more.
For example, to find the HCF of 150 and 60, list factors of both and pick the highest common one: 30.
Vedantu also teaches these concepts interactively—see how factors of a number apply in broader Maths topics.
Related Concepts and Interlinks
Understanding factors helps you easily solve questions in:
- Prime Factorization – master the factor tree method.
- Factors of 75 – compare factors to spot similarities and practice HCF.
- Factors of 60 – see common factors for LCM practice.
We explored factors of 150—from meaning, steps, pairs, prime factorization, to practical uses. Continue practicing with Vedantu to build confidence and speed in such topics!
FAQs on Factors of 150 – Definition, List & Prime Factorization
1. What are the factors of 150?
The factors of 150 are the numbers that divide 150 exactly without leaving a remainder. These are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
2. How do you find the factors of 150?
You can find the factors of 150 using two main methods:
- Division method: Systematically divide 150 by each integer, starting from 1, until you reach 150. If the division results in a whole number, that number is a factor.
- Factor pairs method: Identify pairs of numbers that multiply to 150. Each number in the pair is a factor. For example, 1 x 150, 2 x 75, 3 x 50, etc.
3. What are the prime factors of 150?
The prime factorization of 150 expresses it as a product of only prime numbers. It is 2 x 3 x 52.
4. What are the factor pairs of 150?
The factor pairs of 150 are pairs of numbers that multiply to 150. These are: (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), (10, 15).
5. How many factors does 150 have?
150 has twelve (12) factors.
6. Is 150 a prime or composite number?
150 is a composite number because it has more than two factors.
7. What is the sum of all factors of 150 (excluding 150)?
The sum of all factors of 150, excluding 150 itself, is 222 (1 + 2 + 3 + 5 + 6 + 10 + 15 + 25 + 30 + 50 + 75 = 222).
8. Which factors of 150 are multiples of 5?
The factors of 150 that are also multiples of 5 are: 5, 10, 15, 25, 30, 50, 75, and 150.
9. What are the common factors of 150 and 180?
To find the common factors, list the factors of both numbers and identify the ones they share. The common factors of 150 and 180 are: 1, 2, 3, 5, 6, 10, 15, and 30.
10. How are the factors of 150 used to find its Highest Common Factor (HCF) with another number?
List all the factors of 150 and the factors of the other number. The highest number that appears in both lists is the HCF.
11. Can 150 be expressed as a product of perfect squares?
No, 150 cannot be expressed solely as a product of perfect squares. While 25 (5²) is a factor, there are other factors that are not perfect squares (2,3).
12. Are negative numbers considered factors of 150?
Yes, negative numbers are also considered factors. For every positive factor, there is a corresponding negative factor. For example, if 2 is a factor (2 x 75 = 150), then -2 is also a factor (-2 x -75 = 150).
