Factors of 1264

The numbers that divide 1264 evenly are known as factors of 1264. A factor of 1264 is a number that divides the number without remainder. The factors of 1264 are 1, 2, 4, 8, 16, 79, 158, 316, 632, and 1264.

Negative factors of 1264: -1, -2, -4, -8, -16, -79, -158, -316, -632, and -1264.

Prime factors of 1264: 2 and 79.

Prime factorization of 1264: 2⁴ × 79.

The sum of the factors of 1264: 1 + 2 + 4 + 8 + 16 + 79 + 158 + 316 + 632 + 1264 = 2480

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1264. Identifying the numbers which are multiplied to get the number 1264 is the multiplication method.

Step 1: Multiply 1264 by 1, 1264 × 1 = 1264.

Step 2: Check for other numbers that give 1264 after multiplying     

2 × 632 = 1264    

 4 × 316 = 1264    

 8 × 158 = 1264     

16 × 79 = 1264

Therefore, the positive factor pairs of 1264 are: (1, 1264), (2, 632), (4, 316), (8, 158), (16, 79). All these factor pairs result in 1264. For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 1264 by 1, 1264 ÷ 1 = 1264.

Step 2: Continue dividing 1264 by the numbers until the remainder becomes 0.

1264 ÷ 1 = 1264

1264 ÷ 2 = 632

1264 ÷ 4 = 316

1264 ÷ 8 = 158

1264 ÷ 16 = 79

Therefore, the factors of 1264 are: 1, 2, 4, 8, 16, 79, 158, 316, 632, 1264.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 1264 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1264 ÷ 2 = 632

632 ÷ 2 = 316

316 ÷ 2 = 158

158 ÷ 2 = 79

79 ÷ 79 = 1

The prime factors of 1264 are 2 and 79. The prime factorization of 1264 is: 2⁴ × 79.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 1264 is divided by 2 to get 632.

Step 2: Now divide 632 by 2 to get 316.

Step 3: Then divide 316 by 2 to get 158.

Step 4: Divide 158 by 2 to get 79. Here, 79 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1264 is: 2⁴ × 79.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 1264: (1, 1264), (2, 632), (4, 316), (8, 158), and (16, 79).

• Negative factor pairs of 1264: (-1, -1264), (-2, -632), (-4, -316), (-8, -158), and (-16, -79).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1264 are 1, 2, 4, 8, 16, 79, 158, 316, 632, and 1264.

• Prime factors: The factors which are prime numbers. For example, 2 and 79 are prime factors of 1264.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1264 are (1, 1264), (2, 632), etc.

• Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1264 is 2⁴ × 79.

• Multiple: A multiple of a number is the product of that number and an integer. For example, 1264 is a multiple of 8.