Factors of 150 Explained with Factor Pairs and Steps

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:

1. Start from 1 and move upwards.
   
   1 divides every integer, so 1 is a factor.
2. Try dividing by 2:
   
   150 ÷ 2 = 75 (no remainder), so 2 is a factor.
3. 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
4. Repeat for every number up to 150.
   
5. 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.

1. Divide 150 by 2: 150 ÷ 2 = 75
2. Divide 75 by 3: 75 ÷ 3 = 25
3. Divide 25 by 5: 25 ÷ 5 = 5
4. Divide 5 by 5: 5 ÷ 5 = 1

So, 150 = 2 × 3 × 5 × 5 = 2 × 3 × 5².

Prime Factorization Tree:

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, 150

2. 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!