Factors of a number are a pair of numbers which when multiplied together produce that number. For example the factors of 70 are 10 and 7 because when we multiply 10 with 7 we get the product as 70. So, 10 and 7 are factors of 70. Similarly, there are other numbers than which multiplied together give the result as 70. Those numbers are also called factors of 70. The two numbers which are multiplied together are known as a pair. We can call 10, 7 as a factor pair of 70. Let us find other factor pairs of 70 and carry out prime factorization of 70.

Factors of 70 are written as (10, 7) and (-10, -7). You know that when we multiply two negative numbers, the product is a positive number. When we multiply -10 x -7, we get the product as 70. It means that we can consider both positive and negative factor pairs for number 70. It is essential to remember that the factor pairs of 70 can only be whole numbers or integers. Whole numbers can be positive or negative. Decimals and fractions are not considered as factors of a number.

Prime Factorization of 70

In mathematics, the prime factorization of positive integers are the prime numbers that divide that number exactly, without a remainder. The prime factorization of a positive number is the series of the integer’s prime factors with their multiples. The process that determines these factors is known as prime factorization. Prime factors of a number are those prime numbers that when multiplied together give the original number. Below find an illustrated example of prime factorization of the number 70.

As you can see, 70 when divided by 2, 5 or 7 gives no remainder. These three numbers are integers and prime numbers. They are also called composite numbers. Prime factorization of a number is the determination of a set of prime integers which when multiplied together give the original number or integer. It is clear that prime numbers are numbers that can divide a number without a remainder. We can call this type of division as the perfect division.

So, it means that 70 is divisible by 2, 5, and 7. They are proper or prime divisors of 70.

What Are The Factors of 70?

When we want to find out the factors of 70, in other words, we are finding out other numbers that when multiplied together give the product as 70. To find the factors of 70, we have to follow some steps.

Let us write the number 70 first. Now, we have to find two number that give the result as 70, as a result of multiplication. Let us start by writing,

1 x 70 = 70

2 x 35 = 70

5 x 14 = 70

10 x 7 = 70

Let us consider the numbers 2 and 35.

As you know that 2 is a prime number- it has only two factors 1 and 2. It is not possible to factorize these numbers further, as 2 x 1 =2

Take the number 35. It is a composite number – it can be factorized further, as 5 x 7 x 1

Hence, the factorization of 70 is written as,

70 = 7 x 5 x 2 x 1.

Let us consider the numbers 5 and 14.

As you know that 5 is a prime number- it has only two factors 1 and 5. It is not possible to factorize these numbers further, as 5 x 1 =5

Take the number 14. It is a composite number – it can be factorized further, as 2 x 7 x 1

Hence, the factorization of 70 is written as,

70 = 7 x 5 x 2 x 1.

No matter which factors of 70 you take, the final answer will always come down to,

70 = 7 x 5 x2 x 1.

When asked to find out the total number of factors of 70, you have to write down all the multiples of 70 such as,

Factors of 70 are: 1, 2, 5,7,14, 10, 35 and 70 = 8 factors.

The positive and negative factors pairs of 70 are as follows:

FAQ (Frequently Asked Questions)

1. Who invented Factorization?

Factorization has always been an interesting topic from centuries. It was first considered by ancient Greek mathematicians. The Greeks introduced the basic theorem of maths, which says that every positive integer or whole number can be factored or broken down further into smaller numbers. This breaking down of a number into smaller numbers or its multiples is known as factorization. It is interesting to note that a number can have only integers or whole numbers as its factors. Decimals and fractions cannot be factors. However, a number can have positive as well as negative numbers as its factors.

2. How do we use factorization?

Factorization can be applied in many things. For instance, in performing arithmetic operations. When we group the factors of an original number, it becomes easier for us to multiple. You can also find out factors by finding the difference in two squares, difference in two cubes. Another method to use factorization is to find the least common multiple or the greatest common factor. For performing all these operations you have to make use of prime numbers. As you know, factors of a number are the numbers you multiply to get the original number. The two numbers are known as factor pairs.