GCF & LCM Calculator
Find Greatest Common Factor and Least Common Multiple with detailed steps
Greatest Common Factor (GCF)
Find the largest number that divides all given numbers
💡 Try These Examples:
Least Common Multiple (LCM)
Find the smallest number that is a multiple of all given numbers
💡 Try These Examples:
Find Both GCF and LCM
Calculate both values at once with detailed comparisons
💡 Try These Examples:
Find All Factors
List all factors of given numbers and identify common factors
💡 Try These Examples:
📖 How to Use This Calculator
- GCF (Greatest Common Factor): The largest number that divides all given numbers evenly
- LCM (Least Common Multiple): The smallest number that all given numbers divide into evenly
- Multiple Methods: Choose from different calculation methods to see various approaches
- Add Numbers: Calculate GCF/LCM for 2 or more numbers (up to 10)
- Step-by-Step: See detailed explanations of each calculation step
- Visual Aids: Prime factorization trees and factor highlighting
- Quick Examples: Try pre-loaded examples to understand the concepts
Percentages Explained
A complete guide to calculating percentages, finding the percent of a number, and working out percent change – with formulas, real‑life examples & practice questions.
What is a percentage?
A percentage is a way of expressing a part of a whole as a fraction of 100. The word comes from the Latin per centum, meaning “by the hundred.” Writing 45 % is equivalent to the fraction 45⁄100 or the decimal 0.45.
How to calculate a percentage
To find what percentage one number is of another, use the formula:
Percentage = (Part / Whole) × 100%
Example: In a class of 30 students, 12 are left‑handed. What percentage are left‑handed?
(12 / 30) × 100 = 40%
Finding the percent of a number
To find p% of a number N:
p% of N = (p / 100) × N
Example: What is 15 % of AED 260?
0.15 × 260 = AED 39.
Calculating percent change
Percent change tells you how much a value has increased or decreased relative to its original amount.
Percent Change = ((New - Original) / Original) × 100%
- Percent increase – result is positive.
- Percent decrease – result is negative.
Example: A phone case drops in price from AED 80 to AED 60.
((60 - 80) / 80) × 100 = -25%. The price decreased by 25 %.
Quick‑fire examples
Example 1 – Test score
You answered 37 out of 50 questions correctly. What’s your percentage score?
Solution: (37 / 50) × 100 = 74%.
Example 2 – Discount
A shirt originally costs AED 120. It’s on sale for 35 % off. What’s the sale price?
Solution: Discount = 0.35 × 120 = AED 42 → Sale price = AED 78.
Practice questions
Try these problems. Reveal the solutions when you’re ready.
1. What is 22 % of 450?
0.22 × 450 = 99
2. A laptop increases in price from AED 3,200 to AED 3,520. Find the percent increase.
((3520 - 3200) / 3200) × 100 ≈ 10%
3. 18 is what percent of 72?
(18 / 72) × 100 = 25%
Still stuck on percentages?
Book a personalised session with our expert maths tutors. In‑person at our Dubai centre or online worldwide.
Get Help with PercentagesFrequently Asked Questions
What’s the easiest way to find 10 % of any number?
Simply move the decimal point one place to the left. For example, 10 % of 480 = 48.
How do I convert a percentage to a fraction?
Write the percentage over 100 and simplify. 75 % = 75⁄100 = 3⁄4.
What’s the difference between percent increase and markup?
Percent increase uses the original amount as the base. Markup often uses cost price as the base while percent increase may use selling price depending on context.
What is the Greatest Common Factor (GCF)?
The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF), of two or more whole numbers is the largest positive integer that divides each of the numbers exactly without leaving a remainder.
How to find the Greatest Common Factor (GCF)?
There are several methods:
- **Listing Factors:** List all factors for each number and then identify the largest factor common to all of them.
- **Prime Factorization:** Find the prime factorization of each number. Multiply all the common prime factors, taking the lowest power for each common prime.
- **Euclidean Algorithm:** This iterative method is efficient for larger numbers. Divide the larger number by the smaller number, then divide the divisor by the remainder. Repeat until the remainder is zero. The last non-zero remainder is the GCF.
What is a common factor?
A common factor of two or more numbers is any number that divides evenly into all of them. For example, the common factors of 12 and 18 are 1, 2, 3, and 6.
Can the GCF of two numbers be greater than either number?
No. The Greatest Common Factor (GCF) of two numbers can never be greater than the smallest of the two numbers. It will always be less than or equal to the smallest number.
What is the GCF of 12 and 18?
The factors of 12 are {1, 2, 3, 4, 6, 12}. The factors of 18 are {1, 2, 3, 6, 9, 18}. The greatest common factor is 6.
What is the GCF of 24 and 36?
The factors of 24 are {1, 2, 3, 4, 6, 8, 12, 24}. The factors of 36 are {1, 2, 3, 4, 6, 9, 12, 18, 36}. The greatest common factor is 12.
What is the GCF of 8 and 12?
The factors of 8 are {1, 2, 4, 8}. The factors of 12 are {1, 2, 3, 4, 6, 12}. The greatest common factor is 4.
What is the GCF of 6 and 8?
The factors of 6 are {1, 2, 3, 6}. The factors of 8 are {1, 2, 4, 8}. The greatest common factor is 2.
What is the GCF of 6 and 9?
The factors of 6 are {1, 2, 3, 6}. The factors of 9 are {1, 3, 9}. The greatest common factor is 3.
What is the GCF of 12 and 16?
The factors of 12 are {1, 2, 3, 4, 6, 12}. The factors of 16 are {1, 2, 4, 8, 16}. The greatest common factor is 4.
What is the GCF of 12 and 20?
The factors of 12 are {1, 2, 3, 4, 6, 12}. The factors of 20 are {1, 2, 4, 5, 10, 20}. The greatest common factor is 4.
What is the GCF of 4 and 6?
The factors of 4 are {1, 2, 4}. The factors of 6 are {1, 2, 3, 6}. The greatest common factor is 2.
What is the GCF of 10 and 8?
The factors of 10 are {1, 2, 5, 10}. The factors of 8 are {1, 2, 4, 8}. The greatest common factor is 2.
What is the GCF of 15 and 20?
The factors of 15 are {1, 3, 5, 15}. The factors of 20 are {1, 2, 4, 5, 10, 20}. The greatest common factor is 5.
What is the GCF of 16 and 24?
The factors of 16 are {1, 2, 4, 8, 16}. The factors of 24 are {1, 2, 3, 4, 6, 8, 12, 24}. The greatest common factor is 8.
What is the GCF of 24 and 32?
The factors of 24 are {1, 2, 3, 4, 6, 8, 12, 24}. The factors of 32 are {1, 2, 4, 8, 16, 32}. The greatest common factor is 8.
What is the Least Common Factor?
The term "Least Common Factor" is not a standard mathematical concept in the same way GCF or LCM are. If it refers to the smallest common divisor, then for any set of positive integers, the least common factor is always 1.
What is the Least Common Multiple (LCM)?
The Least Common Multiple (LCM) of two or more non-zero whole numbers is the smallest positive integer that is a multiple of all the numbers.
How to find the Least Common Multiple (LCM)?
There are several methods:
- **Listing Multiples:** List the multiples of each number until you find the first common multiple.
- **Prime Factorization:** Find the prime factorization of each number. For each prime factor, take the highest power that appears in any of the factorizations and multiply them together.
- **Using GCF:** For two numbers 'a' and 'b', LCM(a, b) = (a × b) / GCF(a, b).
What is a common multiple?
A common multiple of two or more numbers is any number that is a multiple of all of them. For example, common multiples of 6 and 8 include 24, 48, 72, etc.
What is the LCM of 8 and 12?
Multiples of 8: {8, 16, 24, 32, ...}. Multiples of 12: {12, 24, 36, ...}. The least common multiple is 24.
What is the LCM of 6 and 8?
Multiples of 6: {6, 12, 18, 24, ...}. Multiples of 8: {8, 16, 24, 32, ...}. The least common multiple is 24.
What is the LCM of 6 and 9?
Multiples of 6: {6, 12, 18, 24, ...}. Multiples of 9: {9, 18, 27, ...}. The least common multiple is 18.
What is the LCM of 9 and 12?
Multiples of 9: {9, 18, 27, 36, ...}. Multiples of 12: {12, 24, 36, ...}. The least common multiple is 36.
What is the LCM of 4 and 10?
Multiples of 4: {4, 8, 12, 16, 20, ...}. Multiples of 10: {10, 20, 30, ...}. The least common multiple is 20.
What is the LCM of 4 and 6?
Multiples of 4: {4, 8, 12, ...}. Multiples of 6: {6, 12, 18, ...}. The least common multiple is 12.
What is the LCM of 3 and 4?
Multiples of 3: {3, 6, 9, 12, ...}. Multiples of 4: {4, 8, 12, ...}. The least common multiple is 12.
What is the LCM of 10 and 12?
Multiples of 10: {10, 20, 30, 40, 50, 60, ...}. Multiples of 12: {12, 24, 36, 48, 60, ...}. The least common multiple is 60.
What is the LCM of 3 and 5?
Since 3 and 5 are prime numbers, their LCM is their product: 3 × 5 = 15.
Is 0 ever used when finding GCF or LCM?
For GCF, GCF(a, 0) = |a|. However, LCM involving 0 is typically undefined because 0 has infinitely many multiples (0, 0, 0, ...), and there is no smallest non-zero common multiple.
Which method is fastest for large numbers?
For finding the GCF of large numbers, the Euclidean Algorithm is generally the most efficient. For LCM, once the GCF is found, the relationship LCM(a, b) = (a × b) / GCF(a, b) provides a fast way to calculate it.
