Factors Of 90 – Definition And Prime Factorization - Vedantu

The concept of factors of 90 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Learning about factors helps you solve questions related to divisibility, prime factorization, LCM, HCF, and more.

What Are Factors of 90?

A factor of 90 is any whole number that divides 90 exactly without leaving a remainder. In mathematics, factors are often used to split numbers into smaller, manageable pieces. You’ll find this concept applied in areas such as finding prime numbers, calculating the LCM and HCF of numbers, and simplifying fractions.

Key Formula for Factors of 90

Here’s the standard way to represent the prime factors of 90: \( 90 = 2 \times 3^2 \times 5 \)

Complete List and Pair Factors of 90

Factors of 90 include all positive integers that divide 90 exactly. The positive factors are:

Factor	Pair Factor
1	90
2	45
3	30
5	18
6	15
9	10

Negative factors are also possible (e.g., -1 × -90 = 90), but in most school-level problems, we focus on positive factors of 90.

How to Find Factors of 90: Step-by-Step

1. Start with 1 and continue up to 90. Check each number: does it divide 90 evenly?
2. If yes, write down both that number and its pair factor (90 divided by that number).
3. List them all in order: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
4. Stop when you repeat previously found numbers in reverse (since factor pairs are mirrored).

Prime Factorization & Factor Tree of 90

Let’s break 90 into its prime factors. This process is called prime factorization.

1. 90 ÷ 2 = 45 (2 is a prime factor)
2. 45 ÷ 3 = 15 (3 is a prime factor)
3. 15 ÷ 3 = 5 (another 3 is used)
4. 5 is a prime number, so we stop.

So, 90 = 2 × 3 × 3 × 5 = 2 × 32 × 5.

Speed Trick or Vedic Shortcut

Here’s a quick tip: if you recall that 90 is divisible by 2, 3, and 5, just use those primes in order. For example, check divisibility by easy rules:

• 90 ends in 0 so it's divisible by 2 and 5.
• Sum the digits: 9 + 0 = 9 → divisible by 3.

This allows you to immediately write prime factorization and quickly build the factor list in exams. Tricks like this are discussed in Vedantu live classes to help students boost calculation speed.

Try These Yourself

• List all factors of 90 between 10 and 50.
• Check if 18 is a factor of 90.
• Is 7 a factor of 90? Show your working.
• Find the sum of all positive factors of 90.

Frequent Errors and Misunderstandings

• Forgetting to include 1 and 90 as factors.
• Mixing factor pairs and prime factors.
• Thinking a number is a factor just because it is "close" to 90 (like 8 or 7).

Relation to Other Concepts

The idea of factors of 90 connects closely with concepts like factors and multiples, LCM and HCF, and prime factorization. Mastering this will make calculations with related topics much easier!

Classroom Tip

A simple way to remember factors: draw a factor tree. Build the prime factorization (2, 3, and 5 for 90), then multiply them in all possible combinations to get every factor. Vedantu’s teachers often use this trick onscreen so students can visualize and memorize factor sets easily.

Wrapping It All Up

We explored factors of 90—from definition, formula, steps, and tricks, all the way to relations with LCM and HCF. Practice listing factors of different numbers. For more practice and live explanations, join Vedantu’s interactive lessons and become confident in solving factorization problems quickly.

Explore more about factors and related topics here:

• Factors of 60
• Factors of 72
• LCM and HCF
• Prime Numbers