Factors of 1568

The numbers that divide 1568 evenly are known as factors of 1568. A factor of 1568 is a number that divides the number without remainder. The factors of 1568 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 196, 224, 392, 784, and 1568.

Negative factors of 1568: -1, -2, -4, -7, -8, -14, -16, -28, -56, -112, -196, -224, -392, -784, and -1568.

Prime factors of 1568: 2 and 7.

Prime factorization of 1568: 2⁶ × 7.

The sum of factors of 1568: 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 56 + 112 + 196 + 224 + 392 + 784 + 1568 = 3418.

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

1. Finding factors using multiplication
2. Finding factors using the 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 1568. Identifying the numbers which are multiplied to get the number 1568 is the multiplication method.

Step 1: Multiply 1568 by 1, 1568 × 1 = 1568.

Step 2: Check for other numbers that give 1568 after multiplying

2 × 784 = 1568

4 × 392 = 1568

7 × 224 = 1568

8 × 196 = 1568

14 × 112 = 1568

16 × 98 = 1568

28 × 56 = 1568

Therefore, the positive factor pairs of 1568 are: (1, 1568), (2, 784), (4, 392), (7, 224), (8, 196), (14, 112), (16, 98), (28, 56). For every positive factor, there is a negative factor.

Dividing the given numbers with 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 simple division method -

Step 1: Divide 1568 by 1, 1568 ÷ 1 = 1568.

Step 2: Continue dividing 1568 by the numbers until the remainder becomes 0.

1568 ÷ 1 = 1568

1568 ÷ 2 = 784

1568 ÷ 4 = 392

1568 ÷ 7 = 224

1568 ÷ 8 = 196

1568 ÷ 14 = 112

1568 ÷ 16 = 98

1568 ÷ 28 = 56

Therefore, the factors of 1568 are: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 196, 224, 392, 784, 1568.

The factors can be found by dividing it with a 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 1568 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1568 ÷ 2 = 784

784 ÷ 2 = 392

392 ÷ 2 = 196

196 ÷ 2 = 98

98 ÷ 2 = 49

49 ÷ 7 = 7

7 ÷ 7 = 1

The prime factors of 1568 are 2 and 7. The prime factorization of 1568 is: 2⁶ × 7.

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

Step 1: Firstly, 1568 is divided by 2 to get 784.

Step 2: Now divide 784 by 2 to get 392.

Step 3: Then divide 392 by 2 to get 196.

Step 4: Divide 196 by 2 to get 98.

Step 5: Divide 98 by 2 to get 49. Step 6: Divide 49 by 7 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1568 is: 2⁶ × 7.

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 1568: (1, 1568), (2, 784), (4, 392), (7, 224), (8, 196), (14, 112), (16, 98), (28, 56).

• Negative factor pairs of 1568: (-1, -1568), (-2, -784), (-4, -392), (-7, -224), (-8, -196), (-14, -112), (-16, -98), (-28, -56).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1568 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 196, 224, 392, 784, and 1568.

• Prime factors: The factors which are prime numbers. For example, 2 and 7 are prime factors of 1568.

• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1568 is 2⁶ × 7.

• 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 1568 are (1, 1568), (2, 784), etc.

• Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the target number. For example, using pairs to find factors of 1568.