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106 LearnersLast updated on September 24, 2025
GCF of 3 and 16
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 3 and 16.
What is the GCF of 3 and 16?
The greatest common factor of 3 and 16 is 1. The largest divisor of two or more numbers is called the GCF of the numbers.
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 3 and 16?
To find the GCF of 3 and 16, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 3 and 16 by Using Listing of factors
Steps to find the GCF of 3 and 16 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 3 = 1, 3. Factors of 16 = 1, 2, 4, 8, 16.
Step 2: Now, identify the common factors of them Common factors of 3 and 16: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 3 and 16 is 1.
GCF of 3 and 16 Using Prime Factorization
To find the GCF of 3 and 16 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 3: 3 = 3 Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 2^4
Step 2: Now, identify the common prime factors There are no common prime factors other than 1.
Step 3: Multiply the common prime factors The Greatest Common Factor of 3 and 16 is 1.
GCF of 3 and 16 Using Division Method or Euclidean Algorithm Method
Find the GCF of 3 and 16 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 16 by 3 16 ÷ 3 = 5 (quotient), The remainder is calculated as 16 − (3×5) = 1 The remainder is 1, not zero, so continue the process
Step 2: Now divide the previous divisor (3) by the previous remainder (1) Divide 3 by 1 3 ÷ 1 = 3 (quotient), remainder = 3 − (1×3) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 3 and 16 is 1.
Common Mistakes and How to Avoid Them in GCF of 3 and 16
Finding GCF of 3 and 16 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 3, students may mention 6, 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 a factor that is not common to both numbers.
To avoid this confusion, students should list all the common factors, even if it's just 1.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of numbers.
However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
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 greater than 1
Students may assume that the GCF of two numbers will always be greater than 1. But that's not true if the numbers are co-prime.
To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 3 and 16 Examples
Problem 1
A farmer has 3 apple trees and 16 orange trees. He wants to organize them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
We should find the GCF of 3 and 16 The GCF of 3 and 16 is 1. There will be 1 tree in each row, as they cannot be grouped together equally with more than 1 tree per row.
Explanation
As the GCF of 3 and 16 is 1, the farmer can only place 1 tree in each row.
Problem 2
A baker has 3 loaves of bread and 16 croissants. She wants to pack them into boxes with the same number of items in each box, using the largest possible number of items per box. How many items will be in each box?
GCF of 3 and 16 The GCF is 1. So each box will have 1 item.
Explanation
There are 3 loaves of bread and 16 croissants.
To find the total number of items in each box, we should find the GCF of 3 and 16.
There will be 1 item in each box.
Problem 3
A gardener has 3 rose bushes and 16 tulip bulbs. She wants to plant them in groups with the same number of plants, using the largest possible number of plants per group. What should be the number of plants in each group?
For calculating the largest equal group size, we need to calculate the GCF of 3 and 16 The GCF of 3 and 16 is 1. Each group will have 1 plant.
Explanation
For calculating the largest group size first, we need to calculate the GCF of 3 and 16, which is 1.
The number of plants in each group will be 1.
Problem 4
A florist has two flower arrangements, one with 3 roses and another with 16 daisies. She wants to divide them into the longest possible equal arrangements, without any flowers left over. What should be the number of flowers in each arrangement?
The florist needs the longest possible equal arrangement GCF of 3 and 16 The GCF is 1. So, the longest arrangement will have 1 flower.
Explanation
To find the longest arrangement of flowers, 3 roses and 16 daisies, respectively, we have to find the GCF of 3 and 16, which is 1.
The longest arrangement will have 1 flower.
Problem 5
If the GCF of 3 and ‘b’ is 1, and the LCM is 48, find ‘b’.
The value of ‘b’ is 48.
Explanation
GCF x LCM = product of the numbers
1 × 48 = 3 × b
48 = 3b
b = 48 ÷ 3
= 16
FAQs on the Greatest Common Factor of 3 and 16
1.What is the LCM of 3 and 16?
2.Is 3 a prime number?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 16?
5.Are 3 and 16 co-prime numbers?
Important Glossaries for GCF of 3 and 16
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, 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 factor of 3 is 3 itself.
- Co-prime Numbers: Two numbers are co-prime if their greatest common factor is 1. For example, 3 and 16 are co-prime.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 16 is divided by 3, the remainder is 1.
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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.
