Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a 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 1512, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 1512 evenly are known as factors of 1512.
A factor of 1512 is a number that divides the number without a remainder.
The factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, and 1512.
Negative factors of 1512: -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -27, -28, -36, -42, -54, -56, -63, -72, -84, -108, -126, -168, -189, -216, -252, -378, -504, -756, and -1512.
Prime factors of 1512: 2, 3, and 7.
Prime factorization of 1512: 23 × 33 × 7.
The sum of factors of 1512: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 18 + 21 + 24 + 27 + 28 + 36 + 42 + 54 + 56 + 63 + 72 + 84 + 108 + 126 + 168 + 189 + 216 + 252 + 378 + 504 + 756 + 1512 = 4423
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1512. Identifying the numbers which are multiplied to get the number 1512 is the multiplication method.
Step 1: Multiply 1512 by 1, 1512 × 1 = 1512.
Step 2: Check for other numbers that give 1512 after multiplying
2 × 756 = 1512
3 × 504 = 1512
4 × 378 = 1512
6 × 252 = 1512
7 × 216 = 1512
9 × 168 = 1512
12 × 126 = 1512
14 × 108 = 1512
18 × 84 = 1512
21 × 72 = 1512
24 × 63 = 1512
27 × 56 = 1512
28 × 54 = 1512
36 × 42 = 1512
Therefore, the positive factor pairs of 1512 are: (1, 1512), (2, 756), (3, 504), (4, 378), (6, 252), (7, 216), (8, 189), (9, 168), (12, 126), (14, 108), (18, 84), (21, 72), (24, 63), (27, 56), (28, 54), and (36, 42).
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 1512 by 1, 1512 ÷ 1 = 1512.
Step 2: Continue dividing 1512 by the numbers until the remainder becomes 0.
1512 ÷ 1 = 1512
1512 ÷ 2 = 756
1512 ÷ 3 = 504
1512 ÷ 4 = 378
1512 ÷ 6 = 252
1512 ÷ 7 = 216
1512 ÷ 8 = 189
1512 ÷ 9 = 168
1512 ÷ 12 = 126
1512 ÷ 14 = 108
1512 ÷ 18 = 84
1512 ÷ 21 = 72
1512 ÷ 24 = 63
1512 ÷ 27 = 56
1512 ÷ 28 = 54
1512 ÷ 36 = 42
Therefore, the factors of 1512 are: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, and 1512.
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 1512 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1512 ÷ 2 = 756
756 ÷ 2 = 378
378 ÷ 2 = 189
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 1512 are 2, 3, and 7.
The prime factorization of 1512 is: 23 × 33 × 7.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1512 is divided by 2 to get 756.
Step 2: Now divide 756 by 2 to get 378.
Step 3: Then divide 378 by 2 to get 189.
Step 4: Divide 189 by 3 to get 63.
Step 5: Divide 63 by 3 to get 21.
Step 6: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1512 is: 23 × 33 × 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 1512: (1, 1512), (2, 756), (3, 504), (4, 378), (6, 252), (7, 216), (8, 189), (9, 168), (12, 126), (14, 108), (18, 84), (21, 72), (24, 63), (27, 56), (28, 54), and (36, 42).
Negative factor pairs of 1512: (-1, -1512), (-2, -756), (-3, -504), (-4, -378), (-6, -252), (-7, -216), (-8, -189), (-9, -168), (-12, -126), (-14, -108), (-18, -84), (-21, -72), (-24, -63), (-27, -56), (-28, -54), and (-36, -42).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A teacher has 1512 pencils and wants to distribute them equally among 7 classes. How many pencils will each class get?
Each class will get 216 pencils.
To divide the pencils equally, we need to divide the total pencils by the number of classes.
1512/7 = 216
A rectangular garden has an area of 1512 square meters and a width of 18 meters. What is the length of the garden?
The length of the garden is 84 meters.
To find the length of the garden, we use the formula, Area = length × width
1512 = length × 18
To find the value of length, we need to divide 1512 by 18.
1512/18 = length
Length = 84.
There are 9 teams in a tournament, and 1512 medals are to be distributed equally. How many medals will each team receive?
Each team will receive 168 medals.
To find the medals each team receives, divide the total medals by the number of teams.
1512/9 = 168
A library has 1512 books, and they need to be arranged in 27 equal stacks. How many books will each stack have?
Each stack will have 56 books.
Divide the total books by the number of stacks to find the number of books in each stack.
1512/27 = 56
A baker has 1512 cookies and wants to pack them in boxes containing 42 cookies each. How many boxes will be needed?
36 boxes will be needed.
To find the number of boxes needed, divide the total cookies by the number of cookies per box.
1512/42 = 36
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.