Factors Of 100 - Vedantu

The concept of factors of 100 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding the factors of 100 makes calculations with division, LCM, HCF, and multiples much easier, and helps students solve word problems quickly and accurately. Mastering this topic boosts confidence in number theory chapters, which is why practicing with factors—like those of 100—is so important for foundational maths.

What Are Factors of 100?

A factor of 100 is a whole number that divides 100 exactly, without leaving a remainder. In other words, if you multiply two whole numbers and get 100 as the result, both of those numbers are factors of 100. You’ll find this concept applied in areas such as multiples, divisibility, LCM and HCF (GCF), and when simplifying fractions in maths.

List of All Factors of 100

The complete list of factors of 100 (positive only, as commonly used in school maths) is:

• 1
• 2
• 4
• 5
• 10
• 20
• 25
• 50
• 100

These are all the numbers that divide 100 exactly—no remainder!

How to Find Factors of 100

Here are the most reliable ways to find all factors of 100, step by step:

1. Start with 1 (since 1 is always a factor of every whole number).
2. Check each whole number up to 100: If 100 ÷ that number = a whole number (no remainder), it’s a factor.
3. Continue until you reach 100 itself (every number is a factor of itself).

Quick List by Division:

Divisor	100 ÷ Divisor	Remainder	Is Factor?
1	100	0	Yes
2	50	0	Yes
4	25	0	Yes
5	20	0	Yes
10	10	0	Yes
20	5	0	Yes
25	4	0	Yes
50	2	0	Yes
100	1	0	Yes

Prime Factorization of 100

Prime factorization means expressing 100 as a product of its prime numbers.

The prime factors of 100 are 2 and 5.

Here’s the step-by-step breakdown:

1. 100 ÷ 2 = 50 2. 50 ÷ 2 = 25 3. 25 ÷ 5 = 5 4. 5 ÷ 5 = 1

So, the prime factorization of 100 is 2 × 2 × 5 × 5, or written using exponents: 22 × 52.

Factor Pairs of 100

Factor pairs are two numbers that multiply together to give 100. Practicing factor pairs helps with area, perimeter, and word-problem questions in exams. Here’s a compact table:

Pair #	First Factor	Second Factor	Product
1	1	100	100
2	2	50	100
3	4	25	100
4	5	20	100
5	10	10	100

Speed Trick or Vedic Shortcut

Here’s a quick trick to check if a number is a factor of 100:

1. Divide 100 by your number.
2. If the result is a whole number (integer), it’s a factor.
3. If you get a remainder, it is NOT a factor.

Tip: Notice that any factor of 100 will end in 0 or 5, or divide 100 evenly.

Memorizing the factor pairs and prime factorization is a favorite strategy shared in Vedantu’s live math classes to boost calculation speed during revision or exams.

Try These Yourself

• List all even factors of 100.
• Find all odd factors of 100.
• Is 8 a factor of 100?
• Write the sum of all factors of 100.
• Find the LCM and HCF of 50 and 100 (using factors).

Frequent Errors and Misunderstandings

• Assuming 8 or 3 are factors of 100 (100 ÷ 8, 100 ÷ 3 give remainders).
• Confusing factors with multiples (e.g., thinking 200 is a factor of 100—actually, 100 is a factor of 200).
• Skipping 1 or the number itself (100) as factors.
• Not pairing factors (forgetting (10,10) is a valid pair).

Relation to Other Concepts

The idea of factors of 100 connects closely with LCM and HCF, and factor trees. Mastering factors helps you easily find common divisors, reduce fractions to lowest terms, and solve word-problems about grouping or sharing.

Classroom Tip

A quick way to remember the factors of 100 is to use the rule—“If a number divides 100 with no remainder, it’s a factor.” Make a table or color the factors in a number chart for fast visual learning. Vedantu’s teachers often use real-life objects (like 100 rupees) to show all possible groups, making maths practical and fun!

We explored factors of 100—from definitions, factor pairs, prime factorization, and mistakes, to how they relate to other maths topics. Continue practicing with Vedantu to become confident in solving problems using this concept, and try linking factors to everyday numbers you use!

Related Vedantu Resources

• Factors of a Number
• Prime Factors
• Factor Tree
• LCM and HCF