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Last updated on May 2nd, 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 and arranging things. In this topic, we will learn about the factors of 840, how they are used in real life, and tips to learn them quickly.
The numbers that divide 840 evenly are known as factors of 840.
A factor of 840 is a number that divides the number without a remainder.
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840.
Negative factors of 840: -1, -2, -3, -4, -5, -6, -7, -8, -10, -12, -14, -15, -20, -21, -24, -28, -30, -35, -40, -42, -56, -60, -70, -84, -105, -120, -140, -168, -210, -280, -420, and -840.
Prime factors of 840: 2, 3, 5, and 7.
Prime factorization of 840: (23 x 3 x 5 x 7).
The sum of factors of 840: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 20 + 21 + 24 + 28 + 30 + 35 + 40 + 42 + 56 + 60 + 70 + 84 + 105 + 120 + 140 + 168 + 210 + 280 + 420 + 840 = 2,232
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 840. Identifying the numbers which are multiplied to get the number 840 is the multiplication method.
Step 1: Multiply 840 by 1, 840 × 1 = 840.
Step 2: Check for other numbers that give 840 after multiplying
(2 x 420 = 840)
(3 x 280 = 840)
(4 x 210 = 840)
(5 x 168 = 840)
(6 x 140 = 840)
(7 x 120 = 840)
(8 x 105 = 840)
(10 x 84 = 840)
(12 x 70 = 840)
(14 x 60 = 840)
(15 x 56 = 840)
(20 x 42 = 840)
(21 x 40 = 840)
(24 x 35 = 840)
(28 x 30 = 840)
Therefore, the positive factor pairs of 840 are: (1, 840), (2, 420), (3, 280), (4, 210), (5, 168), (6, 140), (7, 120), (8, 105), (10, 84), (12, 70), (14, 60), (15, 56), (20, 42), (21, 40), (24, 35), and (28, 30).
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 which result in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 840 by 1, 840 ÷ 1 = 840.
Step 2: Continue dividing 840 by the numbers until the remainder becomes 0.
840 ÷ 1 = 840
840 ÷ 2 = 420
840 ÷ 3 = 280
840 ÷ 4 = 210
840 ÷ 5 = 168
840 ÷ 6 = 140
840 ÷ 7 = 120
840 ÷ 8 = 105
840 ÷ 10 = 84
840 ÷ 12 = 70
840 ÷ 14 = 60
840 ÷ 15 = 56
840 ÷ 20 = 42
840 ÷ 21 = 40
840 ÷ 24 = 35
840 ÷ 28 = 30
Therefore, the factors of 840 are: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840.
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 840 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
840 ÷ 2 = 420
420 ÷ 2 = 210
210 ÷ 2 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 840 are 2, 3, 5, and 7.
The prime factorization of 840 is: (23 x 3 x 5 x 7).
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 840 is divided by 2 to get 420.
Step 2: Now divide 420 by 2 to get 210.
Step 3: Then divide 210 by 2 to get 105.
Step 4: Divide 105 by 3 to get 35.
Step 5: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 840 is: (23 x 3 x 5 x 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.
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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.