Find Hof using prime fraction 77 and 88 60 and 180
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Answer:
180, a positive integer with more divisors than any other smaller positive integer, is also a highly composite number. 180 is a number which is refactorable. In this lesson, we will calculate the factors of 180, prime factors of 180, and factors of 180 in pairs along with solved examples for a better understanding.
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180
Prime Factorization of 180: 180 = 22 × 32 × 5
What Are the Factors of 180?
The number 180 is an even composite number. As it is even, it will have 2 as its factor. To understand why it is composite, let's recall the definition of a composite number. A number is said to be composite if it has more than two factors. Consider the number 19. It has only two factors, 1 and 19. So, it's prime. Now, let's take the case of 60. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. There are more than two factors of 60, hence it's composite. Let's come back to 180. The factors of 180 are all the integers that 180 can be divided into.
How to Calculate the Factors of 180?
We can use different methods like prime factorization and the division method to calculate the factors of 180. In prime factorization, we express 180 as a product of its prime factors and in the division method, we see what numbers divide 180 exactly without a remainder.
Factors of 180 by Prime Factorization
The number 180 is divided by the smallest prime number which divides 180 exactly, i.e., it leaves a remainder of 0. The quotient is then divided by the smallest or second smallest prime number and the process continues till the quotient gets undividable. Let us divide 180 by the prime number 2.
180 ÷ 2 = 90
Now we need to divide the quotient 90 by the next least prime number.
90 ÷ 2 = 45
Now, 45 is a odd number so it is not divisible by 2, but it is divisible by 3.
45 ÷ 3 = 15
Again 15 is divisible by 3.
15 ÷ 3 = 5
5 is a prime number we cannot divide further. Therefore, the prime factors of 180 are 2, 3, and 5 only. Exponentially it can be written as 180 = 22 x 32 x 5