Last updated on July 31st, 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, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 8 and 56.
The greatest common factor of 8 and 56 is 8. 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.
To find the GCF of 8 and 56, a few methods are described below>
Steps to find the GCF of 8 and 56 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 8 = 1, 2, 4, 8.
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56.
Step 2: Now, identify the common factors of them/
Common factors of 8 and 56: 1, 2, 4, 8.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 8.
The GCF of 8 and 56 is 8.
To find the GCF of 8 and 56 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 8: 8 = 2 x 2 x 2 = 2³
Prime Factors of 56: 56 = 2 x 2 x 2 x 7 = 2³ x 7
Step 2: Now, identify the common prime factors.
The common prime factors are: 2 x 2 x 2 = 2³
Step 3: Multiply the common prime factors 2³ = 8.
The Greatest Common Factor of 8 and 56 is 8.
Find the GCF of 8 and 56 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number:
Here, divide 56 by 8 56 ÷ 8 = 7 (quotient), The remainder is calculated as 56 − (8×7) = 0
Since the remainder is zero, the divisor will become the GCF.
The GCF of 8 and 56 is 8.
Finding the GCF of 8 and 56 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
A farmer has 8 apple trees and 56 orange trees. He wants to plant them in equal rows with the largest number of trees per row. How many trees will be in each row?
We should find the GCF of 8 and 56 GCF of 8 and 56
2³ = 8.
There are 8 equal rows.
8 ÷ 8 = 1
56 ÷ 8 = 7
There will be 8 rows, and each row will have 1 apple tree and 7 orange trees.
As the GCF of 8 and 56 is 8, the farmer can make 8 rows.
Now divide 8 and 56 by 8.
Each row gets 1 apple tree and 7 orange trees.
A baker has 8 chocolate cupcakes and 56 vanilla cupcakes. He wants to place them in boxes with the same number of cupcakes in each box, using the largest possible number of cupcakes per box. How many cupcakes will be in each box?
GCF of 8 and 56
2³ = 8.
So each box will have 8 cupcakes.
There are 8 chocolate and 56 vanilla cupcakes.
To find the total number of cupcakes in each box, we should find the GCF of 8 and 56.
There will be 8 cupcakes in each box.
A gardener has 8 meters of rose fencing and 56 meters of tulip fencing. She wants to cut both fences into sections of equal length, using the longest possible length. What should be the length of each section?
For calculating the longest equal length, we have to calculate the GCF of 8 and 56
The GCF of 8 and 56
2³ = 8.
Each section will be 8 meters long.
For calculating the longest length of the fencing sections, first, we need to calculate the GCF of 8 and 56, which is 8. The length of each section of the fencing will be 8 meters.
A carpenter has two wooden planks, one 8 cm long and the other 56 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?
The carpenter needs the longest piece of wood GCF of 8 and 56
2³ = 8.
The longest length of each piece is 8 cm.
To find the longest length of each piece of the two wooden planks, 8 cm and 56 cm, respectively.
We have to find the GCF of 8 and 56, which is 8 cm.
The longest length of each piece is 8 cm.
If the GCF of 8 and ‘b’ is 8, and the LCM is 56, find ‘b’.
The value of ‘b’ is 56.
GCF x LCM = product of the numbers
8 × 56 = 8 × b
448 = 8b
b = 448 ÷ 8 = 56
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.