GCF of 63 and 49
2026-02-28 23:15 Diff
https://brightchamps.com/en-us/math/numbers/gcf-of-63-and-49

147 Learners

Last updated on September 18, 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 63 and 49.

What is the GCF of 63 and 49?

The greatest common factor of 63 and 49 is 7. 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 63 and 49?

To find the GCF of 63 and 49, a few methods are described below 

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

GCF of 63 and 49 by Using Listing of factors

Steps to find the GCF of 63 and 49 using the listing of factors

Step 1: Firstly, list the factors of each number

Factors of 63 = 1, 3, 7, 9, 21, 63.

Factors of 49 = 1, 7, 49.

Step 2: Now, identify the common factors of them Common factors of 63 and 49: 1, 7.

Step 3: Choose the largest factor The largest factor that both numbers have is 7. The GCF of 63 and 49 is 7.

Explore Our Programs

GCF of 63 and 49 Using Prime Factorization

To find the GCF of 63 and 49 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime Factors of each number

Prime Factors of 63: 63 = 3 x 3 x 7 = 3² x 7

Prime Factors of 49: 49 = 7 x 7 = 7²

Step 2: Now, identify the common prime factors The common prime factor is: 7

Step 3: Multiply the common prime factors 7 = 7. The Greatest Common Factor of 63 and 49 is 7.

GCF of 63 and 49 Using Division Method or Euclidean Algorithm Method

Find the GCF of 63 and 49 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 63 by 49 63 ÷ 49 = 1 (quotient),

The remainder is calculated as 63 - (49×1) = 14 The remainder is 14, not zero, so continue the process

Step 2: Now divide the previous divisor (49) by the previous remainder (14) Divide 49 by 14 49 ÷ 14 = 3 (quotient), remainder = 49 - (14×3) = 7 The remainder is 7, not zero, so continue the process

Step 3: Divide 14 by 7 14 ÷ 7 = 2 (quotient), remainder = 14 - (7×2) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 63 and 49 is 7.

Common Mistakes and How to Avoid Them in GCF of 63 and 49

Finding GCF of 63 and 49 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 baker has 63 chocolate cookies and 49 vanilla cookies. He wants to put them into boxes with the same number of cookies in each box, using the largest possible number of cookies per box. How many cookies will be in each box?

Okay, lets begin

We should find the GCF of 63 and 49 GCF of 63 and 49 is 7.

There are 7 cookies in each box. 63 ÷ 7 = 9 49 ÷ 7 = 7

There will be 9 boxes with chocolate cookies and 7 with vanilla cookies, each having 7 cookies.

Explanation

As the GCF of 63 and 49 is 7, the baker can put 7 cookies in each box.

Now divide 63 and 49 by 7.

There will be 9 boxes with chocolate cookies and 7 with vanilla cookies.

Well explained 👍

Problem 2

An artist has 63 blue beads and 49 red beads. He wants to create necklaces using the largest possible number of beads per necklace. How many beads will be in each necklace?

Okay, lets begin

GCF of 63 and 49 is 7. So each necklace will have 7 beads.

Explanation

There are 63 blue beads and 49 red beads.

To find the total number of beads in each necklace, we should find the GCF of 63 and 49.

There will be 7 beads in each necklace.

Well explained 👍

Problem 3

A gardener has 63 meters of wire and 49 meters of rope. He wants to cut both 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 63 and 49.

The GCF of 63 and 49 is 7.

The pieces will be 7 meters long.

Explanation

For calculating the longest length of the wire and rope first, we need to calculate the GCF of 63 and 49, which is 7.

The length of each piece will be 7 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 63 cm long and the other 49 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 63 and 49 is 7.

The longest length of each piece is 7 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 63 cm and 49 cm, respectively, we have to find the GCF of 63 and 49, which is 7 cm.

The longest length of each piece is 7 cm.

Well explained 👍

Problem 5

If the GCF of 63 and ‘b’ is 7, and the LCM is 441, find ‘b’.

Okay, lets begin

The value of ‘b’ is 49.

Explanation

GCF x LCM = product of the numbers

7 × 441 = 63 × b

3087 = 63b

b = 3087 ÷ 63 = 49

Well explained 👍

FAQs on the Greatest Common Factor of 63 and 49

1.What is the LCM of 63 and 49?

The LCM of 63 and 49 is 441.

2.Is 63 divisible by 9?

Yes, 63 is divisible by 9 because 63 ÷ 9 = 7.

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 49?

The prime factorization of 49 is 7².

5.Are 63 and 49 prime numbers?

No, 63 and 49 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 63 and 49

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 14 are 1, 2, 7, and 14.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, 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 18 are 2 and 3.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 17 is divided by 5, the remainder is 2 and the quotient is 3.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 63 and 49 is 441.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 63 and 49 is 7, as it is their largest common factor that divides the numbers completely.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.