GCF of 105 and 90
2026-02-28 10:35 Diff
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Last updated on August 14, 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 to schedule events. In this topic, we will learn about the GCF of 105 and 90.

What is the GCF of 105 and 90?

The greatest common factor of 105 and 90 is 15. 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 105 and 90?

To find the GCF of 105 and 90, a few methods are described below -

  1. Listing Factors
  2. Prime Factorization
  3. Long Division Method / by Euclidean Algorithm

GCF of 105 and 90 by Using Listing of Factors

Steps to find the GCF of 105 and 90 using the listing of factors:

Step 1: Firstly, list the factors of each number.

Factors of 105 = 1, 3, 5, 7, 15, 21, 35, 105.

Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.

Step 2: Now, identify the common factors of them. Common factors of 105 and 90: 1, 3, 5, 15.

Step 3: Choose the largest factor. The largest factor that both numbers have is 15. The GCF of 105 and 90 is 15.

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GCF of 105 and 90 Using Prime Factorization

To find the GCF of 105 and 90 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number. Prime Factors of 105: 105 = 3 x 5 x 7 Prime Factors of 90: 90 = 2 x 3 x 3 x 5

Step 2: Now, identify the common prime factors. The common prime factors are: 3 x 5

Step 3: Multiply the common prime factors. 3 x 5 = 15. The Greatest Common Factor of 105 and 90 is 15.

GCF of 105 and 90 Using Division Method or Euclidean Algorithm Method

Find the GCF of 105 and 90 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number. Here, divide 105 by 90. 105 ÷ 90 = 1 (quotient), The remainder is calculated as 105 − (90×1) = 15. The remainder is 15, not zero, so continue the process.

Step 2: Now divide the previous divisor (90) by the previous remainder (15). Divide 90 by 15. 90 ÷ 15 = 6 (quotient), remainder = 90 − (15×6) = 0.

The remainder is zero, the divisor will become the GCF. The GCF of 105 and 90 is 15.

Common Mistakes and How to Avoid Them in GCF of 105 and 90

Finding the GCF of 105 and 90 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.

Problem 1

A teacher has 105 markers and 90 highlighters. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?

Okay, lets begin

We should find the GCF of 105 and 90. GCF of 105 and 90: 3 x 5 = 15.

There are 15 equal groups. 105 ÷ 15 = 7 90 ÷ 15 = 6

There will be 15 groups, and each group gets 7 markers and 6 highlighters.

Explanation

As the GCF of 105 and 90 is 15, the teacher can make 15 groups. Now divide 105 and 90 by 15. Each group gets 7 markers and 6 highlighters.

Well explained 👍

Problem 2

A school has 105 red chairs and 90 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?

Okay, lets begin

GCF of 105 and 90: 3 x 5 = 15. So each row will have 15 chairs.

Explanation

There are 105 red and 90 blue chairs. To find the total number of chairs in each row, we should find the GCF of 105 and 90. There will be 15 chairs in each row.

Well explained 👍

Problem 3

A tailor has 105 meters of red ribbon and 90 meters of blue 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?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 105 and 90. The GCF of 105 and 90: 3 x 5 = 15. The ribbon is 15 meters long.

Explanation

For calculating the longest length of the ribbon, first we need to calculate the GCF of 105 and 90, which is 15. The length of each piece of the ribbon will be 15 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 105 cm long and the other 90 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 105 and 90: 3 x 5 = 15. The longest length of each piece is 15 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 105 cm and 90 cm, respectively, we have to find the GCF of 105 and 90, which is 15 cm. The longest length of each piece is 15 cm.

Well explained 👍

Problem 5

If the GCF of 105 and ‘a’ is 15, and the LCM is 630, find ‘a’.

Okay, lets begin

The value of ‘a’ is 90.

Explanation

GCF x LCM = product of the numbers

15 × 630 = 105 × a

9450 = 105a

a = 9450 ÷ 105 = 90

Well explained 👍

FAQs on the Greatest Common Factor of 105 and 90

1.What is the LCM of 105 and 90?

The LCM of 105 and 90 is 630.

2.Is 105 divisible by 3?

Yes, 105 is divisible by 3 because the sum of its digits (1+0+5=6) is divisible by 3.

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 90?

The prime factorization of 90 is 2 x 3^2 x 5.

5.Are 105 and 90 prime numbers?

No, 105 and 90 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 105 and 90

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.
  • 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 105 are 3, 5, and 7.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 105 is divided by 90, the remainder is 15.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 105 and 90 is 630.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 105 and 90 is 15, as it is their largest common factor that divides the numbers completely.

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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.