What Times What Equals 105

Factors of 105

Factors of 105 are the list of integers that tin can exist evenly divided into 105. There are overall eight factors of 105 amidst which 105 is the biggest factor and i, 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 (seven, 15).

• Factors of 105: 1, 3, 5, 7, xv, 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

1.	What Are the Factors of 105?
2.	How to Summate the Factors of 105?
3.	Factors of 105 by Prime Factorization
iv.	Factors of 105 in Pairs
5.	FAQs on Factors of 105

What Are the Factors of 105?

Factors of 105 are the numbers that split up 105 perfectly without leaving whatsoever balance.

The factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.

How to Calculate the Factors of 105?

To calculate the factors of 105, we tin can use the sectionalisation method. Let's start with i.

105 ÷ 1 leaves remainder 0.

Since 105 is not an even number, 2 does non carve up 105 completely. Thus, information technology leaves a remainder.

105 ÷ 3 leaves remainder 0.

105 ÷ 5 leaves residuum 0.

105 ÷ 7 leaves remainder 0.

105 ÷ fifteen leaves remainder 0.

105 ÷ 21 leaves remainder 0.

105÷ 35 leaves remainder 0.

105 ÷ 105 leaves balance 0.

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

Explore factors using illustrations and interactive examples

• Factors of 75: The factors of 75 are 1, 3, 5, xv, 25 and 75
• Factors of 175: The factors of 15 are one, 3, five, and 15.
• Factors of 35:  The factors of 35 are 1, five, 7, and 35.
• Factors of seventy: The factors of 70 are i, 2, five, vii, 10, 14, 35, and 70.
• Factors of 42: The factors of i, 2, 3, six, 7, xiv, 21, and 42.

Factors of 105 by Prime Factorization

Prime factorization means expressing a blended number as the product of its prime factors.

Prime factorization of 105 = iii × five × vii. We tin can determine the other composite factors of 105 from its prime factors. We can see that 35 is a factor of 105. Similarly, 15 and 21 are also factors of 105.

Factors of 105 in Pairs

The pair of numbers that requite 105 on multiplication are the factors of 105 in pairs. Look at the rainbow below. Nosotros start from i and motility forrard past including the numbers that give us 105 as their product.

We become the following combinations: 1 × 105, 3 × 35, v × 21, and seven × 15.

Tips and Tricks:

• All the numbers have at to the lowest degree two factors. 105 volition have the first factor as 1 and the other factor is 105 itself.
• Factors of 105 are all the possible numbers 105 is divisible past. They may be prime numbers or composite numbers.
• Factors are always integers. They tin can never be fractions or decimals.

Factors of 105 Solved Examples

1. Example 1: 105 students are to be divided into groups such that there are an equal number of students in each group. In how many ways can they be grouped?

   Solution:

   We will use the concept of cistron pairing to carve up 105 students into groups.

   We know that (35, 3), (five, 21), and (7, 15) are the factor pairs of 105.

   Thus, the students tin can be grouped in iii different means.

2. Case 2:Emily has a chocolate box with 105 chocolates in it. She distributed the chocolates amid her classmates. Tin you observe the total number of students if she gives 5 chocolate to each i of them?

   Solution:

   Given, full number of chocolates = 105

   Chocolates given to each educatee = 5

   Thus, the number of students in the class is = 105 ÷ 5 = 21 students.

   Here we tin see the numbers used, i.e. (5,21), is a pair factor of 105.

3. Example three:Is there whatever take chances that yous can split up 105 geometry boxes as among fifty kids?

   Solution:Clearly, the respond is NO! Because 50 is not a factor of 105 and leaves a remainder, so we cannot distribute 105 geometry boxes to l kids equally.

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FAQs on Factors of 105

What are the Factors of 105?

The factors of 105 are 1, 3, 5, 7, fifteen, 21, 35, 105 and its negative factors are -ane, -iii, -5, -7, -15, -21, -35, -105.

How Many Factors of 105 are likewise Factors of 3?

Since, the factors of 105 are ane, 3, 5, seven, fifteen, 21, 35, 105 and the factors of 3 are 1, 3.
Hence, [1, 3] are the common factors of 105 and 3.

What is the Sum of all the Factors of 105?

Sum of all factors of 105 = (iii^{1 + 1} - 1)/(three - 1) × (5^{one + one} - 1)/(5 - 1) × (7^{ane + ane} - 1)/(7 - 1) = 192

What is the Greatest Common Factor of 105 and 97?

The factors of 105 are 1, iii, 5, 7, 15, 21, 35, 105 and the factors of 97 are 1, 97. 105 and 97 have but one mutual factor which is one. This implies that 105 and 97 are co-prime.

Hence, the Greatest Common Factor (GCF) of 105 and 97 is 1.

What are the Pair Factors of 105?

The pair factors of 105 are (1, 105), (three, 35), (five, 21), (7, fifteen).

What Times What Equals 105,

Source: https://www.cuemath.com/numbers/factors-of-105/

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