# Factors of 50

Definition of factors of 50: If a number completely divides 50 with the remainder zero, then that number is called a factor of 50. So we can say that the factors of 50 are the divisors of 50. In this section, we will learn about the factors of 50 and the prime factors of 50.

#### Highlights of Factors of 50

• 50=2×5×5 is the prime factorization of 50.
• The factors of 50 are 1, 2, 5, 10, 25, and 50.
• Prime factors of 50 are 2 and 5.
• Negative factors of 50 are –1, -2, -5, -10, -25, and –50.

#### What are the factors of 50?

Let us write the number 50 multiplicatively in all possible ways. Doing so we have:

 50 = 1×50 ∴ 1, 50 are factors of 50. 50 = 2×25 ∴ 2, 25 are factors of 50 50 = 5×10 ∴ 5, 10 are factors of 50

As we can express 50 multiplicatively in no other way, so we will stop right now. So the factors of 50 are the numbers in brown color.

∴ The factors of 50 are 1, 2, 5, 10, 25, and 50.

#### Pair Factors of 50

 50 = a×b Factors in Pairs (a,b) 50 = 1×50 (1, 50) 50 = 2×25 (2, 25) 50 = 5×10 (5, 10)

Thus the positive pair factors of 50 are (1, 50), (2, 25), and (5, 10).

We know that (a, b) is a pair factor of 50 if and only if (-a, -b) is a negative pair factor of 50. So all the negative pair factors of 50 are (-1, -50), (-2, -25), and (-5, -10).

#### Number of factors of 50

From above we have calculated the factors of 50 which are 1, 2, 5, 10, 25, and 50. Thus the total number of factors of 50 is six.

#### Prime Factors of 50

Note that the factors of 50 are 1, 2, 5, 10, 25, and 50. Among those factors, we notice that only 2 and 5 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 50 are 2 and 5.

Question: What are the factors of 50?

Video Solution:

 Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70 Factors of 80: 1, 2, 4, 8, 10, 20, 40, 80

#### How to find factors of 50?

Now we will determine the factors of 50 by division method. In this method, we will find the numbers that can divide 50 with no remainder. See that

 50/1=50 and the remainder is 0 ∴ 1 and 50 are factors of 50 50/2=25 and the remainder is 0 ∴ 2 and 25 are factors of 50 50/5=10 and the remainder is 0 ∴ 5 and 10 are factors of 50

Note that no numbers other than the numbers in violet color can divide 50. So the numbers in violet color, that is, 1, 2, 5, 10, 25, and 50 are the complete list of factors of 50.