Find the prime factorization of 105 using division by primes. Show work please

Factors of 105 are the list of integers that can be evenly divided into 105. There are overall 8 factors of 105 among which 105 is the biggest factor and 1, 3, 5, 7, 15, 21, 35, and 105 are positive factors. The sum of all factors of 105 is 192 and its factors in Pairs are (1, 105), (3, 35), (5, 21), and (7, 15).

Factors of 105: 1, 3, 5, 7, 15, 21, 35 and 105

Negative Factors of 105: -1, -3, -5, -7, -15, -21, -35 and -105

Prime Factors of 105: 3, 5, 7

Prime Factorization of 105: 3 × 5 × 7 = 3 × 5 × 7

Sum of Factors of 105: 192

Step-by-step explanation:

To calculate the factors of 105, we can use the division method. Let's start with 1.

105 ÷ 1 leaves remainder 0.

Since 105 is not an even number, 2 does not divide 105 completely. Thus, it leaves a remainder.

105 ÷ 3 leaves remainder 0.

105 ÷ 5 leaves remainder 0.

105 ÷ 7 leaves remainder 0.

105 ÷ 15 leaves remainder 0.

105 ÷ 21 leaves remainder 0.

105÷ 35 leaves remainder 0.

105 ÷ 105 leaves remainder 0.

Thus, the factors of 105 that we have obtained are 1, 3, 5, 7, 15, 21, 35, and 105.

Explore factors using illustrations and interactive examples

Factors of 75: The factors of 75 are 1, 3, 5, 15, 25 and 75

Factors of 175: The factors of 15 are 1, 3, 5, and 15.

Factors of 35:  The factors of 35 are 1, 5, 7, and 35.

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

Factors of 42: The factors of 1, 2, 3, 6, 7, 14, 21, and 42.

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45

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