Factors of 364

The factors of 364 are the numbers that divide 364 evenly.

Positive Factors: These are the positive numbers that divide, 364 evenly.
Positive factors are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, and 364.

Negative Factors: The negative values of the factors of 4200 are:
Negative factors are -1, -2, -4, -7, -13, -14, -26, -28, -52, -91, -182, -364

Prime Factors: Prime factors are the prime numbers themselves that, when multiplied together, give 364 as the product.
Prime factors: 2, 7, 13

Prime Factorization: Prime factorization involves breaking 364 into its prime factors.
It is expressed as 2² × 7¹ × 13¹

Table Listing the Factors of 364

This breakdown helps in understanding the various factors of 364, whether they are positive or negative, as well as how prime factorization works for this number.

There are different methods to find the factors of 364.

Methods to Find the Factors of 364:

1. Multiplication Method
2. Division Method
3. Prime Factor and Prime Factorization
4. Factor Tree

The multiplication method finds the pair of factors that give 364 as their product.

Step 1: Find the pair of numbers whose product is 364.

Step 2: The factors are those numbers, which when multiplied, give 364.

Step 3: Make a list of numbers whose product will be 364.

A list of numbers whose products are 364 is given below:

• 1 × 364 = 364
• 2 × 182 = 364
• 4 × 91 = 364
• 7 × 52 = 364
• 13 × 28 = 364
• 14 × 26 = 364

Thus, the factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, and 364.

The division method finds the numbers that fully divide the given number. The steps are given below:

Step 1: Since every number is divisible by 1, 1 will always be a factor.

Example: 364 ÷ 1 = 364

Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.

Thus, the factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, and 364

Multiplying prime numbers to get the given number as their product is called prime factors. A number when it is simplified using the factors of that number and is expressed in the form of prime factors is the prime factorization of a number.

Prime Factors of 364: Number 364 has three prime factors.
Prime factors of 364: 2, 7, 13

To find the prime factors of 364, we can divide 364 with the prime numbers like 2, 7, and 13 from the list of factors of 364.

Step 1: Divide 364 with the prime number 2

• 364 ÷ 2 = 182

Step 2: Divide 182 with the prime number 2

• 182 ÷ 2 = 91

Step 3: Divide 91 with the prime number 7

• 91 ÷ 7 = 13

Step 4: Divide 13 with the prime number 13

• 13 ÷ 13 = 1

Prime Factorization of 364: Prime factorization breaks down the prime factors of 364.

Expressed as 2² × 7¹ × 13¹.

The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.

This tree shows the breakdown of 364 into its prime factors: 2 × 7 × 13.

Positive and Negative Factor Pairs of 364

Factors of 364 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.

Positive Factor Pairs: (1, 364), (2, 182), (4, 91), (7, 52), (13, 28), (14, 26)

Negative Factor Pairs: (-1, -364), (-2, -182), (-4, -91), (-7, -52), (-13, -28), (-14, -26)

Factors: Numbers that can divide another number completely without leaving a remainder.

For example, 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, and 364 are factors of 364.

Negative Factors: The negative counterparts of positive factors. For 364, they are -1, -2, -4, -7, -13, -14, -26, -28, -52, -91, -182, and -364.

Prime Factors: Prime numbers that, when multiplied together, yield the original number. For 364, the prime factors are 2, 7, and 13.

Prime Factorization: The process of expressing a number as a product of its prime factors. For 364, the prime factorization is 2² × 7 × 13.

Multiple: The result of multiplying a number by an integer. For example, 364 is a multiple of 13 because 13 × 28 = 364.