Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1034, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 1034 evenly are known as factors of 1034.
A factor of 1034 is a number that divides the number without remainder.
The factors of 1034 are 1, 2, 517, and 1034.
Negative factors of 1034: -1, -2, -517, and -1034.
Prime factors of 1034: 2 and 517.
Prime factorization of 1034: 2 × 517
The sum of factors of 1034: 1 + 2 + 517 + 1034 = 1554
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify pairs of numbers that are multiplied to give 1034. Identifying the numbers which are multiplied to get the number 1034 is the multiplication method.
Step 1: Multiply 1034 by 1, 1034 × 1 = 1034.
Step 2: Check for other numbers that give 1034 after multiplying. 2 × 517 = 1034
Therefore, the positive factor pairs of 1034 are: (1, 1034) and (2, 517). All these factor pairs result in 1034. 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 a whole number as factors. Factors can be calculated by following the simple division method -
Step 1: Divide 1034 by 1, 1034 ÷ 1 = 1034.
Step 2: Continue dividing 1034 by numbers until the remainder becomes 0.
1034 ÷ 1 = 1034
1034 ÷ 2 = 517
Therefore, the factors of 1034 are: 1, 2, 517, 1034.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 1034 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1034 ÷ 2 = 517
517 ÷ 517 = 1
The prime factors of 1034 are 2 and 517.
The prime factorization of 1034 is: 2 × 517.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1034 is divided by 2 to get 517.
Step 2: 517 is a prime number, so it cannot be divided anymore. So, the prime factorization of 1034 is: 2 × 517.
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 1034: (1, 1034), (2, 517).
Negative factor pairs of 1034: (-1, -1034), (-2, -517).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 4 teams and 1034 participants in a competition. How will they divide the participants equally?
They will get 258 participants each.
To divide the participants equally, we need to divide the total participants by the number of teams.
1034/4 = 258.5, which is not a whole number, hence even division is not possible, but for similar calculations:
1034/2 = 517
A rectangular garden has a width of 2 meters and a total area of 1034 square meters. Find the length?
517 meters.
To find the length of the garden, we use the formula,
Area = length × width
1034 = length × 2
To find the value of length, we need to shift 2 to the left side.
1034/2 = length
Length = 517.
There are 517 boxes and 1034 candies. How many candies will be in each box?
Each box will have 2 candies.
To find the candies in each box, divide the total candies by the boxes.
1034/517 = 2
In a class, there are 1034 students, and 2 groups. How many students are there in each group?
There are 517 students in each group.
Dividing the students by the total groups, we will get the number of students in each group.
1034/2 = 517
1034 toys need to be arranged in 2 shelves. How many toys will go on each shelf?
Each of the shelves has 517 toys.
Divide total toys by shelves.
1034/2 = 517
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.