Factors of 74 Using Prime Factorization
What are the Factors of 74?
The factors of 74 are the numbers that divide 74 evenly, that is, with no remainder as the definition of factors tells us. If we divide 74 by a natural number that will give us 0 as a remainder then the number is a factor of 74.
The number 74 has a total of four factors, which are, 1, 2, 37 and 74.
Factors of 74
Factors of 74 | 1, 2, 37, and 74. |
Factor Pairs of 74 | (1, 74), and (2, 37) |
Prime factorization of 74 | 2 and 37 |
Example: 37 is a factor of 74 because when we divide 74 by 37, it gives us the quotient as 2, and the remainder as 0.
37厂74 2
-74
_____
R0
Here, Quotient = 2
Remainder = 0
So, to check if any number is a factor of 74 or not, divide 74 by that number and verify that the remainder is zero or not.
[Note: If a number is divided by its factor then the quotient obtained is also a factor of that number.]
Factor List of 74
Divisibility rules and division facts are applied to determine whether a number is a factor of 74 or not.
Number | Is the number a factor of 74? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number. | 1 x 74 = 74 |
2 | Yes, 74 is even. | 2 x 37 = 74 |
3 | No, 4 + 7 = 11 is not divisible by 3. | |
4 | No, 74 ÷ 4 = 18 R2 | |
5 | No, the ones digit is not 0 or 5. | |
6 | No, 74 is even but it is not divisible by 3. | |
7 | No, 74 ÷ 7 = 10 R4 | |
8 | No, 74 ÷ 8 = 9 R2 |
We can stop the derivation of factors with this step because the multiplication equations will start to repeat for higher numbers. So, the factors of 74 are the multiplicands of each multiplication equation. Since there are 2 multiplication equations with unique multiplicands, the number 74 has four factors, which are, 1, 2, 37 and 74.
Prime Factors of 74
The number 74 is a composite number, that is, it has more than two numbers as factors. To find the prime factors, first we will divide the number 74 by its smallest prime factor, that is, 2.
74 ÷ 2 = 37
Again, divide it by 2;
37 ÷ 2 = 22.5, not a factor.
Now, divide 37 by the next prime numbers, that is, 3, 5, 7, and so on.
37 ÷ 3 = 12.33, not a factor.
37 ÷ 5 = 7.4, not a factor.
37 ÷ 7 = 5.286, not a factor.
As 37 is also a prime number so let’s check with 37
37 ÷ 37 = 1, is a factor
So, the prime factorization of 74 = 2 x 37.
Therefore, 2, and 37 are the prime factors of the number 74.
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Factor Pairs of 74
The factor pair of a number is a set of two factors of that number whose product is the number itself.
Example: (2, 37) is the factor pair of 37 as 2 x 37 = 74.
Factors of 74 | Factor Pairs of 74 |
|---|---|
1 x 74 | 1, 74 |
2 x 37 | 2, 37 |
Rapid Recall
Factors of 74 are;
Solved Factors of 74 Examples
Example 1: Find the common factors of 18 and 74.
Solution:
Factors of 18 = 1, 2, 3, 6, 9, and 18.
Factors of 74 = 1, 2, 37, and 74.
Therefore, the common factors of 18 and 74 are 1, and 2.
Example 2: Find the common factors of 74 and 10.
Solution:
Factors of 74 = 1, 2, 37, and 74.
Factors of 10 = 1, 2, 5, and 10
Therefore, the common factors of 74 and 10 are 1, and 2.
Example 3: Find the greatest common factor of 37 and 74.
Solution:
Factors of 37 = 1 and 37.
Factors of 74 = 1, 2, 37, and 74.
So the common factors of 37 and 74 are 1 and 37.
Therefore the greatest common factor of 37 and 74 is 37.
Example 4: Archie owns a toy shop. She decides to arrange 74 toys on 2 shelves. How should she arrange the toys so that each shelf has an equal number of toys?
Solution:
Total number of toys = 74
Number of shelves = 2
Number of toys on each shelf can be calculated by dividing the total number of toys by the number of shelves, that is,
\(\frac{74}{2} \)
= \(\frac{37~\times~2}{2} \) [(37,2) is a factor pair of 74]
= 37 [Simplify]
Therefore, Archie should place 37 toys on each shelf to arrange the toys equally on each shelf.
The factors of 74 are 1, 2, 37, and 74.
So, the least factor of 74 is 1, and the greatest factor is 74 itself.
The factors of 74 are 1, 2, 37, and 74.
Sum of the factors = 1 + 2 + 37 + 74 = 114
So, the sum of factors of 74 is 114.
No, 15 is not a factor of 74. This is because when the number 15 divides 74, it leaves the quotient as 4 and the remainder as 14.
The prime factorization of 74 is ‘2 x 37’.
The number 74 has a total of four factors, so it is not a prime number.