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Factors of 361

Factors of 361 are the list of integers that we can split evenly into 361. There are total 3 factors of 361 i.e. 1, 19, 361. The Pair Factors of 361 are (1, 361), (19, 19) and its Prime Factors are 19.

  • All Factors of 361: 1, 19 and 361
  • Negative Factors of 361: -1, -19 and -361
  • Prime Factors of 361: 19
  • Prime Factorization of 361: 192
  • Sum of Factors of 361: 381
1. What Are the Factors of 361?
2. Factors of 361 by Prime Factorization
3. Factors of 361 in Pairs
4. FAQs on Factors of 361
Factors of 361

What are Factors of 361?

Factors of 361 are pairs of those numbers whose products result in 361. These factors are either prime numbers or composite numbers.

How to Find the Factors of 361?

To find the factors of 361, we will have to find the list of numbers that would divide 361 without leaving any remainder.

  • 361/19 = 19; therefore, 19 is a factor of 361.
  • 361/1 = 361; therefore, 1 is a factor of 361 and 361 is also a factor of 361.
Similarly we can find other factors. Hence, the factors of 361 are 1, 19, 361.

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Factors of 361 by Prime Factorization

The number 361 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 361. The first step is to divide the number 361 with the smallest prime factor, here it is 19. We keep dividing until it gives a non-zero remainder.
  • 361 ÷ 19 = 19
  • 19 ÷ 19 = 1

Further dividing 1 by 19 gives a non-zero remainder. So we stop the process and continue dividing the number 1 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

Since, we can't divide any further in this case so we stop.

So, the prime factorization of 361 is 192.

 

Factors of 361 in Pairs

Pair factors of 361 are the pairs of numbers that when multiplied give the product 361. The factors of 361 in pairs are:

  • 1 × 361 = (1, 361)
  • 19 × 19 = (19, 19)

Negative pair factors of 361 are:

  • -1 × -361 = (-1, -361)
  • -19 × -19 = (-19, -19)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 361 Solved Examples

  1. Example 1: How many factors are there for 361?

    Solution:

    The factors of 361 are 1, 19, 361. Therefore, 361 has 3 factors.

  2. Example 2: Find the LCM and Highest Common Factor (HCF) of 361 and 259.

    Solution:

    The factors of 361 are 1, 19, 361 and factors of 259 are 1, 7, 37, 259.

    Therefore, the LCM of 361 and 259 is 93499 and Highest Common Factor (HCF) of 361 and 259 is 1.

  3. Example 3: Find if 1 and 113 are factors of 361.

    Solution:

    When we divide 361 by 113 it leaves a remainder. Therefore, the number 113 is not a factor of 361. All numbers except 113 are factors of 361.

  4. Example 4: Find the product of all the factors of 361.

    Solution:

    Since, the factors of 361 are 1, 19, 361. Therefore, the product of factors = 1 × 19 × 361 = 6859.

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FAQs on Factors of 361

What are the Factors of 361?

The factors of 361 are 1, 19, 361 and its negative factors are -1, -19, -361.

What is the Sum of all Factors of 361?

Since, all factors of 361 are 1, 19, 361 therefore, the sum of its factors is 1 + 19 + 361 = 381.

What are Prime Factors of 361?

The prime factor of 361 is 19.

What is the Greatest Common Factor of 361 and 196?

The factors of 361 are 1, 19, 361 and the factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196. 361 and 196 have only one common factor which is 1. This implies that 361 and 196 are co-prime.

Hence, the Greatest Common Factor (GCF) of 361 and 196 is 1.

How Many Factors of 361 are also common to the Factors of 133?

Since, the factors of 361 are 1, 19, 361 and the factors of 133 are 1, 7, 19, 133.
Hence, [1, 19] are the common factors of 361 and 133.

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