GCF of 16 and 84
2026-02-28 23:22 Diff
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Last updated on September 24, 2025

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 84.

What is the GCF of 16 and 84?

The greatest common factor of 16 and 84 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 84?

To find the GCF of 16 and 84, a few methods are described below

  • Listing Factors
     
  • Prime Factorization
     
  • Long Division Method / by Euclidean Algorithm

GCF of 16 and 84 by Using Listing of Factors

Steps to find the GCF of 16 and 84 using the listing of factors

Step 1: Firstly, list the factors of each number Factors of 16 = 1, 2, 4, 8, 16. Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

Step 2: Now, identify the common factors of them Common factors of 16 and 84: 1, 2, 4.

Step 3: Choose the largest factor The largest factor that both numbers have is 4. The GCF of 16 and 84 is 4.

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GCF of 16 and 84 Using Prime Factorization

To find the GCF of 16 and 84 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 84: 84 = 2 x 2 x 3 x 7 = 22 x 3 x 7

Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 = 2^2

Step 3: Multiply the common prime factors 22 = 4. The Greatest Common Factor of 16 and 84 is 4.

GCF of 16 and 84 Using Division Method or Euclidean Algorithm Method

Find the GCF of 16 and 84 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 84 by 16 84 ÷ 16 = 5 (quotient), The remainder is calculated as 84 − (16×5) = 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 84 is 4.

Common Mistakes and How to Avoid Them in GCF of 16 and 84

Finding GCF of 16 and 84 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.

Problem 1

A gardener has 16 red roses and 84 white roses. She wants to bundle them in equal groups with the largest number of roses in each bundle. How many roses will be in each bundle?

Okay, lets begin

We should find the GCF of 16 and 84 GCF of 16 and 84 is 4. There are 4 equal bundles. 16 ÷ 4 = 4 84 ÷ 4 = 21 There will be 4 bundles, and each bundle gets 4 red roses and 21 white roses.

Explanation

As the GCF of 16 and 84 is 4, the gardener can make 4 bundles.

Now divide 16 and 84 by 4.

Each bundle gets 4 red roses and 21 white roses.

Well explained 👍

Problem 2

A chef has 16 apples and 84 oranges. He wants to arrange them in rows with the same number of fruits in each row, using the largest possible number of fruits per row. How many fruits will be in each row?

Okay, lets begin

GCF of 16 and 84 is 4. So each row will have 4 fruits.

Explanation

There are 16 apples and 84 oranges.

To find the total number of fruits in each row, we should find the GCF of 16 and 84.

There will be 4 fruits in each row.

Well explained 👍

Problem 3

A tailor has 16 meters of red fabric and 84 meters of blue 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?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 16 and 84 The GCF of 16 and 84 is 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 84, which is 4.

The length of each piece of the fabric will be 4 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 16 cm long and the other 84 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?

Okay, lets begin

The carpenter needs the longest piece of wood GCF of 16 and 84 is 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 84 cm, respectively, we have to find the GCF of 16 and 84, which is 4 cm.

The longest length of each piece is 4 cm.

Well explained 👍

Problem 5

If the GCF of 16 and ‘a’ is 4, and the LCM is 336. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 84.

Explanation

GCF x LCM = product of the numbers

4 × 336 = 16 × a

1344 = 16a

a = 1344 ÷ 16

= 84

Well explained 👍

FAQs on the Greatest Common Factor of 16 and 84

1.What is the LCM of 16 and 84?

The LCM of 16 and 84 is 336.

2.Is 16 divisible by 2?

Yes, 16 is divisible by 2 because it is an even number.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 84?

The prime factorization of 84 is 2^2 x 3 x 7.

5.Are 16 and 84 prime numbers?

No, 16 and 84 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 16 and 84

  • 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 28 are 2 and 7.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 9 is divided by 4, the remainder is 1 and the quotient is 2.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 16 and 84 is 336.

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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.