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 714, how they are used in real life, and tips to learn them quickly.
The numbers that divide 714 evenly are known as factors of 714.
A factor of 714 is a number that divides the number without remainder.
The factors of 714 are 1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 102, 119, 153, 238, 357, and 714.
Negative factors of 714: -1, -2, -3, -6, -7, -9, -14, -17, -18, -21, -34, -42, -51, -102, -119, -153, -238, -357, and -714.
Prime factors of 714: 2, 3, 7, and 17.
Prime factorization of 714: 2 × 3 × 7 × 17.
The sum of factors of 714: 1 + 2 + 3 + 6 + 7 + 9 + 14 + 17 + 18 + 21 + 34 + 42 + 51 + 102 + 119 + 153 + 238 + 357 + 714 = 1908.
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 714. Identifying the numbers which are multiplied to get the number 714 is the multiplication method.
Step 1: Multiply 714 by 1, 714 × 1 = 714.
Step 2: Check for other numbers that give 714 after multiplying
2 × 357 = 714
3 × 238 = 714
6 × 119 = 714
7 × 102 = 714
9 × 79.333 (not a factor)
17 × 42 = 714
21 × 34 = 714
Therefore, the positive factor pairs of 714 are: (1, 714), (2, 357), (3, 238), (6, 119), (7, 102), (17, 42), (21, 34).
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 that result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 714 by 1, 714 ÷ 1 = 714.
Step 2: Continue dividing 714 by the numbers until the remainder becomes 0.
714 ÷ 1 = 714
714 ÷ 2 = 357
714 ÷ 3 = 238
714 ÷ 6 = 119
714 ÷ 7 = 102
714 ÷ 9 = 79.
333 (not a factor)
714 ÷ 17 = 42
714 ÷ 21 = 34
Therefore, the factors of 714 are: 1, 2, 3, 6, 7, 17, 21, 34, 42, 102, 119, 238, 357, 714.
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 714 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
714 ÷ 2 = 357
357 ÷ 3 = 119
119 ÷ 7 = 17
17 ÷ 17 = 1
The prime factors of 714 are 2, 3, 7, and 17.
The prime factorization of 714 is: 2 × 3 × 7 × 17.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 714 is divided by 2 to get 357.
Step 2: Now divide 357 by 3 to get 119.
Step 3: Then divide 119 by 7 to get 17.
Here, 17 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 714 is: 2 × 3 × 7 × 17.
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 714: (1, 714), (2, 357), (3, 238), (6, 119), (7, 102), (17, 42), (21, 34).
Negative factor pairs of 714: (-1, -714), (-2, -357), (-3, -238), (-6, -119), (-7, -102), (-17, -42), (-21, -34).
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 6 teams and 714 points. How will they divide the points equally?
Each team will get 119 points.
To divide the points equally, we need to divide the total points by the number of teams.
714/6 = 119
A rectangular garden has a length of 17 meters and the total area is 714 square meters. Find the width?
42 meters.
To find the width of the garden, we use the formula,
Area = length × width
714 = 17 × width
To find the value of width, we need to shift 17 to the left side.
714/17 = width
Width = 42.
There are 21 boxes and 714 marbles. How many marbles will be in each box?
Each box will have 34 marbles.
To find the marbles in each box, divide the total marbles by the number of boxes.
714/21 = 34
In a conference, there are 714 participants and 7 groups. How many participants are there in each group?
There are 102 participants in each group.
Dividing the participants by the total groups, we will get the number of participants in each group.
714/7 = 102
714 apples need to be arranged in 3 baskets. How many apples will go in each basket?
Each of the baskets will have 238 apples.
Divide total apples by the number of baskets.
714/3 = 238
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.