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 the items equally, arranging things, etc. In this topic, we will learn about the factors of 3150, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 3150 evenly are known as factors of 3150.
A factor of 3150 is a number that divides the number without remainder.
The factors of 3150 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 30, 35, 42, 45, 50, 63, 70, 75, 90, 105, 126, 150, 175, 210, 225, 315, 350, 450, 525, 630, 1050, 1575, and 3150.
Negative factors of 3150: -1, -2, -3, -5, -6, -7, -9, -10, -14, -15, -18, -21, -25, -30, -35, -42, -45, -50, -63, -70, -75, -90, -105, -126, -150, -175, -210, -225, -315, -350, -450, -525, -630, -1050, -1575, and -3150.
Prime factors of 3150: 2, 3, 5, and 7.
Prime factorization of 3150: 2 × 3² × 5² × 7.
The sum of factors of 3150: 1 + 2 + 3 + 5 + 6 + 7 + 9 + 10 + 14 + 15 + 18 + 21 + 25 + 30 + 35 + 42 + 45 + 50 + 63 + 70 + 75 + 90 + 105 + 126 + 150 + 175 + 210 + 225 + 315 + 350 + 450 + 525 + 630 + 1050 + 1575 + 3150 = 9360.
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 3150. Identifying the numbers which are multiplied to get the number 3150 is the multiplication method.
Step 1: Multiply 3150 by 1, 3150 × 1 = 3150.
Step 2: Check for other numbers that give 3150 after multiplying
2 × 1575 = 3150
3 × 1050 = 3150
5 × 630 = 3150
6 × 525 = 3150
7 × 450 = 3150
9 × 350 = 3150
10 × 315 = 3150
14 × 225 = 3150
15 × 210 = 3150
18 × 175 = 3150
21 × 150 = 3150
25 × 126 = 3150
30 × 105 = 3150
35 × 90 = 3150
42 × 75 = 3150
45 × 70 = 3150
50 × 63 = 3150
Therefore, the positive factor pairs of 3150 are: (1, 3150), (2, 1575), (3, 1050), (5, 630), (6, 525), (7, 450), (9, 350), (10, 315), (14, 225), (15, 210), (18, 175), (21, 150), (25, 126), (30, 105), (35, 90), (42, 75), (45, 70), (50, 63). For every positive factor, there is a negative factor.
Dividing the given number 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 a simple division method -
Step 1: Divide 3150 by 1, 3150 ÷ 1 = 3150.
Step 2: Continue dividing 3150 by the numbers until the remainder becomes 0.
3150 ÷ 1 = 3150
3150 ÷ 2 = 1575
3150 ÷ 3 = 1050
3150 ÷ 5 = 630
3150 ÷ 6 = 525
3150 ÷ 7 = 450
3150 ÷ 9 = 350
3150 ÷ 10 = 315
3150 ÷ 14 = 225
3150 ÷ 15 = 210
3150 ÷ 18 = 175
3150 ÷ 21 = 150
3150 ÷ 25 = 126
3150 ÷ 30 = 105
3150 ÷ 35 = 90
3150 ÷ 42 = 75
3150 ÷ 45 = 70
3150 ÷ 50 = 63
Therefore, the factors of 3150 are: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 30, 35, 42, 45, 50, 63, 70, 75, 90, 105, 126, 150, 175, 210, 225, 315, 350, 450, 525, 630, 1050, 1575, and 3150.
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 3150 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3150 ÷ 2 = 1575
1575 ÷ 3 = 525
525 ÷ 3 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
The prime factors of 3150 are 2, 3, 5, and 7.
The prime factorization of 3150 is: 2 × 3² × 5² × 7.
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 3150 is divided by 2 to get 1575.
Step 2: Now divide 1575 by 3 to get 525.
Step 3: Then divide 525 by 3 to get 175.
Step 4: Divide 175 by 5 to get 35.
Step 5: Divide 35 by 5 to get 7. Here, 7 is a prime number, and it cannot be divided anymore. So, the prime factorization of 3150 is: 2 × 3² × 5² × 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 3150: (1, 3150), (2, 1575), (3, 1050), (5, 630), (6, 525), (7, 450), (9, 350), (10, 315), (14, 225), (15, 210), (18, 175), (21, 150), (25, 126), (30, 105), (35, 90), (42, 75), (45, 70), (50, 63).
Negative factor pairs of 3150: (-1, -3150), (-2, -1575), (-3, -1050), (-5, -630), (-6, -525), (-7, -450), (-9, -350), (-10, -315), (-14, -225), (-15, -210), (-18, -175), (-21, -150), (-25, -126), (-30, -105), (-35, -90), (-42, -75), (-45, -70), (-50, -63).
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 3150 apples and 7 baskets. How will they divide it equally?
They will get 450 apples each.
To divide the apples equally, we need to divide the total apples by the number of baskets.
3150/7 = 450
A rectangular plot has a width of 30 meters and a total area of 3150 square meters. Find the length?
105 meters.
To find the length of the plot, we use the formula,
Area = length × width
3150 = length × 30
To find the value of the length, we need to shift 30 to the left side.
3150/30 = length
Length = 105.
There are 9 trays and 3150 eggs. How many eggs will be in each tray?
Each tray will have 350 eggs.
To find the eggs in each tray, divide the total eggs by the trays.
3150/9 = 350
A school has 3150 students, and they want to form 25 groups. How many students are there in each group?
There are 126 students in each group.
Dividing the students by the total groups, we will get the number of students in each group.
3150/25 = 126
3150 pages need to be printed in 21 booklets. How many pages will go in each booklet?
Each of the booklets has 150 pages.
Divide total pages by booklets.
3150/21 = 150
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.