Factors of 34 Using Prime Factorization
Factors of 34
Divisor | Is the number a factor of 34? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number. | 1 x 34 = 34 |
2 | Yes, 34 is even. | 2 x 17 = 34 |
3 | No, as 3 + 4 = 7 it is not divisible by 3. | |
4 | No, as 34 ÷ 4 = 8 and the remainder is 2. | |
5 | No, the ones digit is not 0 or 5. | |
6 | No, 34 ÷ 6 = 5 and the remainder is 4 | |
7 | No, 34 ÷ 7 = 4 and the remainder is 6 | |
8 | No, 34 ÷ 8 = 4 and the remainder is 2 |
Prime Factors of 34
The factor tree below illustrates the prime factors of 34:
The prime factorization of 34 is 2 x 17. This means that 2 and 17 are the prime factors of 34.
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Positive Factor Pairs of 34
Positive factors of 34 | Positive factor pairs of 34 |
|---|---|
1 x 34 | (1, 34) |
2 x 17 | (2, 17) |
Rapid Recall
Solved Factors of 34 Examples
Example 1: Find the common factors of 11 and 34.
Solution:
The factors of 11: 1 and 11.
The factors of 34: 1, 2, 17 and 34.
So, the common factor of 11 and 34 is 1.
Hence, 11 and 34 have 1 common factor.
Example 2: Find the common factors of 4 and 34.
Solution:
The factors of 4: 1, 2 and 4.
The factors of 34 are 1, 2, 17 and 34.
So, the common factors of 4 and 34 are 1 and 2.
Hence, 4 and 34 have 2 common factors.
Example 3: Keisha has 18 dolls and her brother Keith has 34 mini robots. How can they arrange their toys in groups, such that each group has the same number of toys and no toy is left behind. Note that robots and dolls cannot be in the same group.
Solution:
To find the number of groups, we need to find the common factors of 18 and 34.
The factors of 18 are 1, 2, 3, 6, 9 and 18.
The factors of 34 are 1, 2, 17 and 34.
So, the common factors of 18 and 34 are 1 and 2.
Hence, dolls and mini robots can be arranged in either groups of 1 or groups of 2.
Example 4: Find the common factors of 10 and 34.
Solution:
The factors of 10 are 1, 2, 5 and 10.
The factors of 34 are 1, 2, 17 and 34.
So, the common factors of 10 and 34 are 1, and 2.
Hence, 10 and 34 have 2 common factors.
Example 5: Find the common factors of 16 and 34.
Solution:
The factors of 16 are 1, 2, 4 and 16.
The factors of 34 are 1, 2, 17 and 34.
So, the common factors of 16 and 34 are 1 and 2.
Hence, 16 and 34 have 2 common factors.
No, when you divide 34 by 6, it will give 4 as a remainder.
The negative factors of 34 are -1, -2, -17 and -34.
Negative factor pairs of 34 are (-1, -34) and (-2, -17).