GCF of 7 and 9
2026-02-28 21:44 Diff
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Last updated on September 11, 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 7 and 9.

What is the GCF of 7 and 9?

The greatest common factor of 7 and 9 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 7 and 9?

To find the GCF of 7 and 9, a few methods are described below -

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

GCF of 7 and 9 by Using Listing of factors

Steps to find the GCF of 7 and 9 using the listing of factors

Step 1: Firstly, list the factors of each number Factors of 7 = 1, 7. Factors of 9 = 1, 3, 9.

Step 2: Now, identify the common factors of them Common factors of 7 and 9: 1.

Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 7 and 9 is 1.

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GCF of 7 and 9 Using Prime Factorization

To find the GCF of 7 and 9 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 7: 7 = 7

Prime Factors of 9: 9 = 3 x 3 = 3²

Step 2: Now, identify the common prime factors The common prime factor is 1.

Step 3: Multiply the common prime factors The Greatest Common Factor of 7 and 9 is 1.

GCF of 7 and 9 Using Division Method or Euclidean Algorithm Method

Find the GCF of 7 and 9 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 9 by 7 9 ÷ 7 = 1 (quotient), The remainder is calculated as 9 − (7×1) = 2

The remainder is 2, not zero, so continue the process

Step 2: Now divide the previous divisor (7) by the previous remainder (2) Divide 7 by 2 7 ÷ 2 = 3 (quotient), remainder = 7 − (2×3) = 1 The remainder is 1, not zero, so continue the process

Step 3: Now divide the previous divisor (2) by the previous remainder (1) Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0

The remainder is zero, the divisor will become the GCF. The GCF of 7 and 9 is 1.

Common Mistakes and How to Avoid Them in GCF of 7 and 9

Finding GCF of 7 and 9 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 7 rose plants and 9 tulip plants. She wants to plant them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?

Okay, lets begin

We should find GCF of 7 and 9 GCF of 7 and 9 is 1.

Therefore, each row will have 1 plant of either type.

Explanation

As the GCF of 7 and 9 is 1, the gardener can only plant one plant in each row. Each row will have either a rose or a tulip plant.

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Problem 2

A teacher has 7 apples and 9 oranges. She wants to arrange them into baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?

Okay, lets begin

GCF of 7 and 9 is 1. So each basket will have 1 fruit.

Explanation

There are 7 apples and 9 oranges. To find the total number of fruits in each basket, we should find the GCF of 7 and 9. There will be 1 fruit in each basket.

Well explained 👍

Problem 3

A tailor has 7 meters of red fabric and 9 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 7 and 9.

The GCF of 7 and 9 is 1.

The fabric pieces will be 1 meter long.

Explanation

For calculating the longest length of the fabric pieces, we need to calculate the GCF of 7 and 9, which is 1. The length of each piece of fabric will be 1 meter.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 7 cm long and the other 9 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 7 and 9 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, 7 cm and 9 cm respectively, we have to find the GCF of 7 and 9, which is 1 cm. The longest length of each piece is 1 cm.

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Problem 5

If the GCF of 7 and ‘a’ is 1, and the LCM is 63. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 9.

Explanation

GCF x LCM = product of the numbers

1 × 63 = 7 × a

63 = 7a

a = 63 ÷ 7 = 9

Well explained 👍

FAQs on the Greatest Common Factor of 7 and 9

1.What is the LCM of 7 and 9?

The LCM of 7 and 9 is 63.

2.Are 7 and 9 co-prime numbers?

Yes, 7 and 9 are co-prime numbers because their only common factor is 1.

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

4.What is the prime factorization of 9?

The prime factorization of 9 is 3².

5.Is 7 a prime number?

Yes, 7 is a prime number because it has only two factors: 1 and itself.

Important Glossaries for GCF of 7 and 9

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 7 are 1 and 7.
  • Prime Numbers: Numbers greater than 1 that have no divisors other than 1 and themselves. For example, 7 is a prime number.
  • Co-prime Numbers: Two numbers are co-prime if their only common factor is 1. For example, 7 and 9 are co-prime.
  • Euclidean Algorithm: A method for finding the GCF of two numbers based on division. It involves dividing and taking remainders until reaching zero.
  • LCM: The smallest common multiple of two or more numbers. For example, the LCM of 7 and 9 is 63.

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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.