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104 LearnersLast updated on September 11, 2025
GCF of 16 and 100
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 16 and 100.
What is the GCF of 16 and 100?
The greatest common factor of 16 and 100 is 4. The largest divisor of two or more numbers is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 16 and 100?
To find the GCF of 16 and 100, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 16 and 100 by Using Listing of Factors
Steps to find the GCF of 16 and 100 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 16 = 1, 2, 4, 8, 16. Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100.
Step 2: Now, identify the common factors of them Common factors of 16 and 100: 1, 2, 4.
Step 3: Choose the largest factor The largest factor that both numbers have is 4. The GCF of 16 and 100 is 4.
GCF of 16 and 100 Using Prime Factorization
To find the GCF of 16 and 100 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 24
Prime Factors of 100: 100 = 2 x 2 x 5 x 5 = 22 x 52
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 = 22
Step 3: Multiply the common prime factors 22 = 4.
The Greatest Common Factor of 16 and 100 is 4.
GCF of 16 and 100 Using Division Method or Euclidean Algorithm Method
Find the GCF of 16 and 100 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 100 by 16 100 ÷ 16 = 6 (quotient), The remainder is calculated as 100 − (16×6) = 4 The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (16) by the previous remainder (4) Divide 16 by 4 16 ÷ 4 = 4 (quotient), remainder = 16 − (4×4) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 16 and 100 is 4.
Common Mistakes and How to Avoid Them in GCF of 16 and 100
Finding GCF of 16 and 100 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 16, students may mention 9, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it indicates an incomplete understanding of factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF Is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 16 and 100 Examples
Problem 1
A gardener has 16 rose bushes and 100 tulip bulbs. She wants to plant them in rows with an equal number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
We should find the GCF of 16 and 100 GCF of 16 and 100 22 = 4.
There are 4 equal rows 16 ÷ 4 = 4 100 ÷ 4 = 25
There will be 4 rows, and each row gets 4 rose bushes and 25 tulip bulbs.
Explanation
As the GCF of 16 and 100 is 4, the gardener can make 4 rows. Now divide 16 and 100 by 4. Each row gets 4 rose bushes and 25 tulip bulbs.
Problem 2
A baker has 16 chocolate muffins and 100 vanilla muffins. She wants to arrange them on trays with the same number of muffins on each tray, using the largest possible number of muffins per tray. How many muffins will be on each tray?
GCF of 16 and 100 22 = 4. So each tray will have 4 muffins.
Explanation
There are 16 chocolate and 100 vanilla muffins. To find the total number of muffins on each tray, we should find the GCF of 16 and 100. There will be 4 muffins on each tray.
Problem 3
A tailor has 16 meters of silk fabric and 100 meters of cotton fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 16 and 100 The GCF of 16 and 100 22 = 4. The fabric is 4 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 16 and 100, which is 4. The length of each piece of fabric will be 4 meters.
Problem 4
A carpenter has two wooden planks, one 16 cm long and the other 100 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 16 and 100 22 = 4. The longest length of each piece is 4 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 16 cm and 100 cm, respectively. We have to find the GCF of 16 and 100, which is 4 cm. The longest length of each piece is 4 cm.
Problem 5
If the GCF of 16 and ‘b’ is 4, and the LCM is 400. Find ‘b’.
The value of ‘b’ is 100.
Explanation
GCF x LCM = product of the numbers
4 × 400 = 16 × b
1600 = 16b
b = 1600 ÷ 16 = 100
FAQs on the Greatest Common Factor of 16 and 100
1.What is the LCM of 16 and 100?
2.Is 16 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 100?
5.Are 16 and 100 prime numbers?
Important Glossaries for GCF of 16 and 100
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 4, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 16 and 100 is 400.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
