Factors of 64

Factors of 64 are 1, 2, 4, 8, 16, 32, and 64 itself. There are positive and negative factors of 64. Factors of 64 can be multiplied to give the product 64. The pair factors of 64 are (8, 8), (2, 32), (4, 16), and (1, 64). We can find prime factors of 64. Additionally, 64 has a maximum factor of 64 and a minimum factor of 1, which can be prime factorized as 2 × 2 × 2 × 2 × 2 × 2 or 2⁶

In this article, we will learn what are factors of 64, how to find factors of 64, prime factorization of 64 and

Factors of a Number is defined as the number which divides the given number exactly without leaving any remainder

What are the Factors of 64?

The factors of 64 are the numbers that can be multiplied collectively to create the product 64. In the case of 64, the factors are 1, 2, 4, 8, 16, 32, and 64. Now let’s multiply these integers pairwise to obtain 64:

• 1 × 64 = 64
• 2 × 32 = 64
• 4 × 16 = 64
• 8 × 8 = 64

So the factors of 64 are 1,2, 4, 8, 16, 32, and 64.

All Factors of 64

Here is a list of all the factors of 64:

Factors of 64 are 1, 2, 4, 8, 16, 32, and 64.

How to Find Factors of 64?

The factors of 64, can be resolved by using two methods:

Factors of 64 using the Multiplication Method

Using the multiplication method, you may discover the factors of 64 by pairing two factors so that their combined multiplicative power equals 64. Let’s see the pairing and get 64.

1. Let’s start with 1 and 64: 1 × 64 = 64
2. After that, 2 and 32: 2 × 32 = 64
3. Now, the next pair is 4 and 32: 4 × 16 = 64
4. The Last pair is 8 with 8: 8 × 8 = 64.

So, the factors of 64 are 1, 2, 4, 8, 16, 32, and 64 is proven by the multiplication method.

Factors of 64 using the Division Method

Using the division method, you can start with 1 and divide 64 by increasing values until you reach 64 to determine the factors of 64. Let’s see the pairing of two numbers;

1. Let’s start with 1: 64 ÷ 1 = 64
2. After that divide 64 by 2: 64 ÷ 2 = 32
3. Now, Divide 64 by 4: 32 ÷ 4 = 8
4. At Last, Divide 64 by 8: 8 ÷ 8 = 1

So, the factors of 64 are 1, 2, 4, 8, 16, 32, and 64 is proven by the Division method.

Prime Factorization of 64

The representation of 64 as a product of its prime factors is known as its prime factorization. So, behind the prime factorization of 64 is the scenario of the number 64 may be written as the product of six prime numbers, each of which is two.

Prime Factorization of 64

So, the prime factorization of 64 is 64 = 2 × 2 × 2 × 2 × 2 × 2 or 2⁶

Prime Factors of 64

As we have seen the prime factorization of 64 is given as

64 = 2 × 2 × 2 × 2 × 2 × 2 or 2⁶

Hence, the Prime factors of 64 is 2 which is raised to power 6.

Factor Tree of 64

Factors of the number 64 is shown graphically by the factor tree. The number 64 is at the top and is broken down into its prime factors by following branches. So,for creating a factor tree of 64 you have to follow some steps that given below;

• Let’s start with number 64.
• 64 splits into 32 and 2.
• After that, 32 is separated into 2 and 16 .
• Then,16 is split into 2 and 8.
• 8 is divided into 2 and 4.
• At last, 4 is further split into 2 and 2.

The factor tree of 64 is shown below:

Factor Tree of 64

Factor Pairs of 64

Factor Pair of 64, is when two integers are multiplied together and provide the original number 64. So, For this process, we will follow the Positive and negative pair factors of 64.

Positive Factor Pairs of 64

Positive Factor Pairs of 64 are tabulated below

Factor Pair	Product
1 × 64 = 64	(1, 64)
2 × 32 = 64	(2, 32)
4 × 16 = 64	(4, 16)
8 × 8 = 64	(8, 8)

Negative Factor Pairs of 64

Negative factor pairs of 64 are tabulated below

Factor Pair	Product
-1 × -64 = 64	(-1, -64)
-2 × -32 = 64	(-2, -32)
-4 × -16 = 64	(-4, -16)
-8 × -8 = 64	(-8, -8)

Factors of 64 – Solved Examples

Example 1: Calculate the Sum of all the factors of 64.

Solution:

Factors of 64 = 1, 2, 4, 8, 16, 32, 64

Sum of Factors of 64 = 1 + 2 + 4 + 8 + 16 + 32 + 64 = 129

Example 2: If a×b=64, find the possible values of a and b.

Solution:

Some of the possible values of a and b are:

• 2 x 32 = 64
• 4 x 16 = 64
• -8 × – 8 = 64
• -1 × -64 = 64

Example 3: John spends 8 hours a day studying. How many days will he need to complete 64 hours?

Solution:

John spends 8 hours a day studying, and he wants to complete 64 hours.

So, Here we use the formula; No. of days = Total Hours/ Hours per day = 64/8 = 8

Therefore, John need 8 days to complete 64 hours.

Example 4: List the common factors between 64, and 100.

Solution:

The Common factors between 64, 100 are:

Factors of 64 = 1, 2, 4, 8, 16, 32, 64

Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100

So, Common Factors between 64, 100 are 1,2, and 4.

Example 5: A whiteboard has a area of 64 square cm. Find the board’s width if its length is 16 cm.

Solution:

The formula for the surface area of a rectangle is given by: Surface Area=Length×Width

Surface Area = 64 cm

Length = 16 cm

64 = 16 × w

You can divide both sides of the equation by 16 to Find the width (w):

W = 64/16

W = 4 cm

So, the width of the whiteboard is 4 cm.

Read More,

• Factors of a Number
• Factors of 36

Factors of 64 – Practice Questions

Q1: Calculate the product of the first three factors of 64.

Q2: List the even factors of 64.

Q3: Determine if 10 is a factor of 64.

Q4: Is 18 a multiple or a factor of 29?

Factors of 64 – Frequently Asked Questions

What is the Largest Factor of 64?

The largest factor of 64 is 64 as

Is 16 a Factor of 64?

16 is a factor of 64 as 16 divides 64 exactly without leaving any remainder

How many Factor 64 have?

The number 64 has a total of 7 factors. These factors are: 1, 2, 4, 8, 16, 32, and 64.

Is 64 a Prime Number?

No, 64 is not a prime number as it has more than 2 factors

List the First Five multiples of 64.

The first five multiples of 64 are given below;

• 64 × 1 = 64
• 64 × 2 = 128
• 64 × 3 = 192
• 64 × 4 = 256
• 64 × 5 = 320

Is 12 a Factor of 64?

No, 12 is not a factor of 64 as 12 doesn’t divide 64 exactly