What are the factors of 70?
The integers that can divide a number completely are known as factors of that number. When a number is divided by its factor the remainder is zero and the quotient is also a factor of that number. The number 70 has a total of eight factors: 1, 2, 5, 7, 10, 14, 35, and 70.
Factor list of the number 70:
70 is a composite number, that is, it has more than two factors.
Therefore, the factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
Prime factors of a number
The factor tree provided in the image is used to learn about the prime factorization of 70, and this is because 70 is a composite number.
Prime factorization of 70 leads us to 2 × 5 × 7, and this means that 2, 5 and 7 are the factors of 70. Additionally, we can say that 2, 5 and 7 are the prime factors of 70.
Positive factor pairs of 70:
The numbers that are multiplied in pairs to produce other natural numbers are known as the factor pairs of the product. Let us look at the factor pairs of 70.
The factor pair of 70, for example, can be (1, 70). Factor pairs of 70 are a set of two numbers when multiplied give the product 70. The following are the positive factor pairs of the number 70:
So the factor pairs for 70 are (1, 70), (2, 35), (5, 14), and (7, 10).
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Solved Factors of 70 Examples
1) Find the common factors of 70 and 30?
Solution:
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
Hence, the common factors of 70 and 30 are 1, 2, 5 and 10.
2) Rachel has 75 legos and Dave has 70 legos. How many groups of Legos can Rachel and Dave make together such that they have an equal number of Legos in each group?
Solution:
To find the number of groups we need to find the common factors of 75 and 70.
The factors of 75 are 1, 3, 5, 15, 25 and 75.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
Hence, the common factors of 70 and 75 are 1 and 5.
Therefore, there can be two groups of Legos that Rachel and Dave can form such that there are an equal number of Legos in each group. They can group them as:
1 lego in each group or,
5 legos in each group.
3) List out the common factors of 70 and 60?
Solution:
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Hence, the common factors of 70 and 60 are 1, 2, 5 and 10.
4) Find the common factors of 70 and 140?
Solution:
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
The factors of 140 are 1, 2, 4, 5 , 7, 8 , 10, 14, 28, 35, 70 and 140.
Hence, the common factors of 70 and 140 are 1, 2, 5, 7, 10, 14, 35 and 70.
5) Find the common factors of 70 and 72?
Solution:
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Hence, the common factors of 70 and 72 are only 1 and 2.
1, 2, 5, 7, 10, 14, 35, and 70 are the factors of 70.
2 × 5 × 7 is the prime factorization of 70.
(1, 70), (2, 35), (5, 14), and (7, 10) are the positive pair factors of 70.
Yes, 35 is a factor of 70. 35 divides 70 exactly and leaves the remainder 0, hence 35 is a factor of 70.