Factors of 1537

The numbers that divide 1537 evenly are known as factors of 1537. A factor of 1537 is a number that divides the number without remainder. The factors of 1537 are 1, 37, 41, and 1537.

Negative factors of 1537: -1, -37, -41, and -1537.

Prime factors of 1537: 37 and 41.

Prime factorization of 1537: 37 × 41.

The sum of factors of 1537: 1 + 37 + 41 + 1537 = 1616

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 1537. Identifying the numbers which are multiplied to get the number 1537 is the multiplication method.

Step 1: Multiply 1537 by 1, 1537 × 1 = 1537.

Step 2: Check for other numbers that give 1537 after multiplying 37 × 41 = 1537

Therefore, the positive factor pairs of 1537 are: (1, 1537), (37, 41). 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 1537 by 1, 1537 ÷ 1 = 1537.

Step 2: Continue dividing 1537 by the numbers until the remainder becomes 0.

1537 ÷ 1 = 1537

1537 ÷ 37 = 41

1537 ÷ 41 = 37

Therefore, the factors of 1537 are: 1, 37, 41, 1537.

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 1537 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1537 ÷ 37 = 41

41 ÷ 41 = 1

The prime factors of 1537 are 37 and 41. The prime factorization of 1537 is: 37 × 41.

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

Step 1: Firstly, 1537 is divided by 37 to get 41.

Step 2: Divide 41 by 41 to get 1. Here, both 37 and 41 are prime numbers, that cannot be divided further. So, the prime factorization of 1537 is: 37 × 41.

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 1537: (1, 1537), (37, 41).

• Negative factor pairs of 1537: (-1, -1537), (-37, -41).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1537 are 1, 37, 41, and 1537.

• Prime factors: The factors which are prime numbers. For example, 37 and 41 are prime factors of 1537.

• 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 1537 are (1, 1537) and (37, 41).

• Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number.

• Division method: A method to find factors by dividing the number by whole numbers until the remainder is zero.