What does the Phrase “Factors of 210” Mean?
The numbers that divide 210 fully without leaving any remainder are considered to be the factors of 210. Another way of explaining the factors of 210 is the integers that when multiplied together in pairs produce a result of 210. The factors or factor pairs of 210 can be positive or negative, but they can’t be expressed in fractions or decimals. Using the prime factorization approach and several solved instances, we will cover the factors of 210, pair factors and prime factors of 210.
Deriving the Factor List of 210
The factors of 210 are the numbers that divide 210 evenly and leave no remainder. Because 210 is an even composite number, it has a lot of other factors other than 1 and 210. 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210 are the factors of 210. The table given below is a derivation of the factors of 210.
Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105 and 210.
Factor Tree of 210
Pair Factors of 210
210 has eight pair factors because it’s a composite number. A pair factor of 210 is a set of two numbers multiplied together to get the number 210. Given below are the factor pairs for 210.
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Rapid Recall
Solved Factors of 210 Examples
Example 1: List out the common factors of 210 and 120.
Solution:
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210 are the factors of 210.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120 are the factors of 120.
Using the data given above, we can list the common factors of 210 and 120 and they are as follows: 1, 2, 3, 5, 6, 10, 15, and 30.
Example 2: Find the 210 and 209 common factors.
Solution:
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210 are the factors of 210.
209 factors are 1, 11, 19, and 209.
As a result, the common factor between 210 and 209 is 1.
Example 3: There were 10 marbles in the red jar and 21 marbles in the green jar. Try to divide the marbles in the jar such that the product of both the numbers in each jar is 210 and the number of marbles in each jar is almost equal.
Solution:
Let’s take a look at the list of the factor pairs of 210
(1, 210)
(2, 105)
(3, 70)
(5, 42)
(6, 35)
(7, 30)
(10, 21)
(14, 15)
Out of the given set of factor pairs only (14, 15) is the factor pair which is almost equal and also gives 210 as the product. So, either place 14 marbles in the red jar and 15 marbles in the green jar or place 15 marbles in the green jar and 14 marbles in the red jar.
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210 are the factors of 210.
2 x 3 x 5 x 7 is the prime factorization of 210.
When 210 is divided by 70, we get 3 as the quotient and the remainder as zero. Therefore, 70 can be considered a factor of 210.
(1, 210), (2, 105), (3, 70), (5, 42), (6, 35), (7, 30), (10, 21), and (14, 15) are the pair factors of 210.