Last updated on August 5th, 2025
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 4 and 16.
The greatest common factor of 4 and 16 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, which is always positive.
To find the GCF of 4 and 16, a few methods are described below:
Steps to find the GCF of 4 and 16 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 4 = 1, 2, 4.
Factors of 16 = 1, 2, 4, 8, 16.
Step 2: Now, identify the common factors of them.
Common factors of 4 and 16: 1, 2, 4.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 4.
The GCF of 4 and 16 is 4.
To find the GCF of 4 and 16 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 4: 4 = 2 x 2 = 2²
Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 2⁴
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 4 and 16 is 4.
Find the GCF of 4 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 4 16 ÷ 4 = 4 (quotient), remainder = 16 − (4×4) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 4 and 16 is 4.
Finding the GCF of 4 and 16 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A baker has 4 loaves of bread and 16 muffins. She wants to pack them into boxes with the largest number of items in each box. How many items will be in each box?
We should find the GCF of 4 and 16 GCF of 4 and 16
2² = 4.
There are 4 equal groups
4 ÷ 4 = 1
16 ÷ 4 = 4
There will be 4 groups, and each box gets 1 loaf of bread and 4 muffins.
As the GCF of 4 and 16 is 4, the baker can make 4 groups.
Now divide 4 and 16 by 4.
Each box gets 1 loaf of bread and 4 muffins.
A gardener has 4 small pots and 16 large pots. They want to arrange them in rows with the same number of pots in each row, using the largest possible number of pots per row. How many pots will be in each row?
GCF of 4 and 16
2² = 4.
So each row will have 4 pots.
There are 4 small and 16 large pots. To find the total number of pots in each row, we should find the GCF of 4 and 16.
There will be 4 pots in each row.
A builder has 4 meters of wood and 16 meters of cable. He wants to cut both 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 4 and 16
The GCF of 4 and 16
2² = 4.
The length of each piece is 4 meters.
For calculating the longest length of the wood and cable first, we need to calculate the GCF of 4 and 16, which is 4.
The length of each piece will be 4 meters.
A mechanic has two metal rods, one 4 cm long and the other 16 cm long. He wants to cut them into the longest possible equal pieces, without any metal left over. What should be the length of each piece?
The mechanic needs the longest piece of metal GCF of 4 and 16
2² = 4.
The longest length of each piece is 4 cm.
To find the longest length of each piece of the two metal rods, 4 cm and 16 cm, respectively.
We have to find the GCF of 4 and 16, which is 4 cm.
The longest length of each piece is 4 cm.
If the GCF of 4 and ‘b’ is 4, and the LCM is 16. Find ‘b’.
The value of ‘b’ is 16.
GCF x LCM = product of the numbers
4 × 16 = 4 × b
64 = 4b
b = 64 ÷ 4 = 16
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.
: She loves to read number jokes and games.