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108 LearnersLast updated on October 3, 2025
GCF of 16 and 25
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 16 and 25.
What is the GCF of 16 and 25?
The greatest common factor of 16 and 25 is 1.
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 25?
To find the GCF of 16 and 25, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 16 and 25 by Using Listing of factors
Steps to find the GCF of 16 and 25 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 16 = 1, 2, 4, 8, 16. Factors of 25 = 1, 5, 25.
Step 2: Now, identify the common factors of them Common factor of 16 and 25: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 16 and 25 is 1.
GCF of 16 and 25 Using Prime Factorization
To find the GCF of 16 and 25 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 = 2^4 Prime Factors of 25: 25 = 5 x 5 = 5^2.
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Multiply the common prime factors Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 16 and 25 is 1.
GCF of 16 and 25 Using Division Method or Euclidean Algorithm Method
Find the GCF of 16 and 25 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 25 by 16 25 ÷ 16 = 1 (quotient), The remainder is calculated as 25 − (16×1) = 9 The remainder is 9, not zero, so continue the process.
Step 2: Now divide the previous divisor (16) by the previous remainder (9) 16 ÷ 9 = 1 (quotient), remainder = 16 − (9×1) = 7.
Step 3: Now divide the previous divisor (9) by the previous remainder (7) 9 ÷ 7 = 1 (quotient), remainder = 9 − (7×1) = 2.
Step 4: Now divide the previous divisor (7) by the previous remainder (2) 7 ÷ 2 = 3 (quotient), remainder = 7 − (2×3) = 1 Step 5: Now divide the previous divisor (2) by the previous remainder (1) 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 16 and 25 is 1.
Common Mistakes and How to Avoid Them in GCF of 16 and 25
Finding GCF of 16 and 25 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 3 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, which is 1 in this case.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers.
It is crucial to remember that 1 is always a factor, especially when numbers are co-prime.
Mistake 4
Using Multiples instead of factors
Students confuse between 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 a non-zero number
Students may assume that the GCF of two numbers will always be a number other than 1.
But it's not true, especially if the numbers are co-prime like 16 and 25.
To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 16 and 25 Examples
Problem 1
A gardener has 16 tulip bulbs and 25 daffodil bulbs. She wants to plant them in rows with an equal number of bulbs per row, using the largest possible number of bulbs per row. How many bulbs will be in each row?
We should find the GCF of 16 and 25, The GCF of 16 and 25 is 1.
There will be 1 row with 16 tulip bulbs and 25 daffodil bulbs.
Explanation
As the GCF of 16 and 25 is 1, the gardener can plant one row with all the bulbs of each type, as they cannot be grouped further.
Problem 2
A school has 16 red flags and 25 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 16 and 25 is 1.
So each row will have 1 flag from each type.
Explanation
There are 16 red and 25 blue flags.
To find the total number of flags in each row, we should find the GCF of 16 and 25.
There will be 1 flag of each color in each row.
Problem 3
A tailor has 16 meters of silk ribbon and 25 meters of cotton ribbon. She wants to cut both ribbons 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 25.
The GCF of 16 and 25 is 1.
The ribbon is 1 meter long.
Explanation
For calculating the longest length of the ribbon first we need to calculate the GCF of 16 and 25, which is 1.
The length of each piece of the ribbon will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 16 cm long and the other 25 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 25 is 1.
The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 16 cm and 25 cm, respectively.
We have to find the GCF of 16 and 25, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 16 and ‘a’ is 1, and the LCM is 400. Find ‘a’.
The value of ‘a’ is 25.
Explanation
GCF x LCM = product of the numbers 1 × 400 = 16 × a 400 = 16a a = 400 ÷ 16 = 25
FAQs on the Greatest Common Factor of 16 and 25
1.What is the LCM of 16 and 25?
2.Is 16 divisible by 4?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 25?
5.Are 16 and 25 prime numbers?
Important Glossaries for GCF of 16 and 25
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 25 are 1, 5, and 25.
- 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 16 are 2.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 25 is divided by 16, the remainder is 9.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 16 and 25 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.
