###### Asked in AlgebraFactoring and Multiples

Algebra

Factoring and Multiples

# What are the common factors and greatest common factor of 128?

## Answer

###### Wiki User

###### March 20, 2009 7:01AM

There is neither a greatest common factor nor common factors of a single number, such as 128, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor.

## Related Questions

###### Asked in Factoring and Multiples

### What is the greatest common factor of 128 and 245?

A factor is a divisor - a number that will evenly divide into
another number. The greatest common factor of two or more numbers
is the largest factor that both numbers have in common.
One way to determine the common factors and greatest common
factor is to find all the factors of the numbers and compare
them.
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
The factors of 245 are 1, 5, 7, 35, 49, and 245.
The only common factor is 1. Therefore, the greatest common
factor is 1.

###### Asked in Factoring and Multiples

### What is the greatest common factor of 48 and 128?

A factor is a divisor - a number that will evenly divide into
another number. The greatest common factor of two or more numbers
is the largest factor that both numbers have in common.
One way to determine the common factors and greatest common
factor is to find all the factors of the numbers and compare
them.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
The common factors are 1, 2, 4, 8, and 16. Therefore, the
greatest common factor is 16.
Factors of 48 are 1, 2, 4, 6, 8, 12, 24, and 48
Factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128
The GCF of 48 and 128 is 8

###### Asked in Factoring and Multiples

### What is the greatest common factor of 306?

There is not a greatest common factor of a single number, such
as 306, because there cannot be a greatest common factor without
two or more numbers to compare. Common factors are factors that the
numbers being compared have in common. The greatest common factor
is the largest factor that all the numbers being compared have in
common.
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153,
and 306.
The prime factors of 306 are 2, 3, 3, and 17.
Examples:
The greatest common factor of 27 and 306 is 9.
The greatest common factor of 128 and 306 is 2.
The greatest common factor of 306 and 765 is 153.

###### Asked in Factoring and Multiples

### What is the greatest common factor of 48 80 and 128?

Answer: 16
One way to determine the greatest common factor is to find all
the factors of the numbers and compare them.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
The common factors are 1, 2, 4, 8, and 16. Therefore, the
greatest common factor is 16.
The greatest common factor can also be calculated by identifying
the common prime factors and multiplying them together.
The prime factors of 48 are 2, 2, 2, 2, and 3.
The prime factors of 80 are 2, 2, 2, 2, and 5.
The prime factors of 128 are 2, 2, 2, 2, 2, 2, and 2.
The prime factors in common are 2, 2, 2, and 2, so the greatest
common factor is 2 x 2 x 2 x 2 = 16.
Another way to approach this is to look at the differences
between the numbers. The greatest common factor of two or more
numbers cannot be larger than the smallest difference between the
numbers. The difference between 48 and 80 is 32. The difference
between 80 and 128 is 48. Also, the greatest common factor must be
a factor of the differences between the numbers. If we find the
greatest common factor of 32 and 48, we will have the greatest
common factor of 48, 80, and 128. The difference between 32 and 48
is 16, so the greatest possible common factor between 32 and 48 is
16. Since 16 is a factor of both 32 and 48, it is their greatest
common factor, and thus the greatest common factor of 48, 80, and
128.

###### Asked in Factoring and Multiples

### What is the greatest common factor of 128 and 4880?

Answer: 16
One way to determine the greatest common factor is to find all
the factors of the numbers and compare them.
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
The factors of 4880 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 61, 80,
122, 244, 305, 488, 610, 976, 1220, 2440, and 4880.
The common factors are 1, 2, 4, 8, and 16. Therefore, the
greatest common factor is 16.
The greatest common factor can also be calculated by identifying
the common prime factors and multiplying them together.
The prime factors of 128 are 2, 2, 2, 2, 2, 2, and 2.
The prime factors of 4880 are 2, 2, 2, 2, 5, and 61.
The prime factors in common are 2, 2, 2, and 2, so the greatest
common factor is 2 x 2 x 2 x 2 = 16.
Another method is to use the Euclidean algorithm.
4880 ÷ 128 = 38 remainder 16
128 ÷ 16 = 8 with no remainder
Therefore, since there was no remainder when dividing by 16, the
greatest common factor of 128 and 4880 is 16.