Factors of 192 Using Prime Factorization
What are the Factors of 192?
Factors of 192 are those integers that divide 192 without leaving any remainder or we can say factors of 192 will divide 192 exactly. The factors of 192 cannot be decimals or fractions.
Factors of 192
Factors | Factors pairs | Prime factorization |
|---|---|---|
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192 | (1, 192), (2, 96), (3, 64) (4, 48), (6,32), (8, 24), (12, 16) | 192 = 2 \(\times \) 2 \(\times \) 2 \(\times \) 2 \(\times \) 2 \(\times \) 2 \(\times \) 3 |
Factor List for Number 192
Divisor | Is the number a factor of 192 ? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 × 192 = 192 |
2 | Yes, 192 is even. | 2 × 96 = 192 |
3 | Yes, 1 + 9 + 2 = 12 is divisible by 3 | 3 × 64 = 192 |
4 | Yes, 192 ÷ 4 = 48 R0 | 4 × 48 = 192 |
5 | No, ones digit is not 0 or 5. | - |
6 | Yes, 192 is even and is divisible by 3. | 6 × 32 = 192 |
7 | No, 192 ÷ 7 = 27 R3 | - |
8 | Yes, 192 ÷ 8 = 24 R0 | 8 × 24 = 192 |
9 | No, 1 + 9 + 2 = 12 is not divisible by 9 | - |
10 | No, ones digit is not 0. | - |
11 | No, 192 ÷ 11 = 17 R5 | - |
12 | Yes, 192 ÷ 12 = 16 R0 | 12 × 16 = 192 |
13 | No, 192 ÷ 13 = 14 R10 | - |
14 | No, 192 ÷ 14 = 13 R10 | - |
15 | No, 192 ÷ 15 = 12 R12 | - |
16 | No, 192 ÷ 16 = 12 R0 | 16 × 12 = 192 |
Here, we can see that the factor pair (12, 16) have repeated. Hence, we can stop checking further as we have derived all the factors of 192.
Factors of 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
Prime Factorization of 192
The factor tree of 192 can be written as:
From the factor tree we can see that the prime factorization of 192 is: 2 \(\times \) 2 \(\times \) 2 \(\times \) 2 \(\times \) 2 \(\times \) 2 \(\times \) 3 = \(2^6~\times~3 \).
This means that 2 and 3 are the prime factors of 192.
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Factor Pairs of 192
A factor pair of 192 is a pair of factors of 192 which when multiplied together result in 192.
Factors of 192: 1 ,2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192.
Positive factors of 192 | Positive pair factors of 192 |
|---|---|
1 \(\times \) 192 | (1, 192) |
2 \(\times \) 96 | (2, 96) |
3 \(\times \) 64 | (3, 64) |
4 \(\times \) 48 | (4, 48) |
6 \(\times \) 32 | (6, 32) |
8 \(\times \) 24 | (8, 24) |
12 \(\times \) 16 | (12, 16) |
Rapid Recall
Solved Factors of 192 Examples
Example 1: Find the common factors of 196 and 192.
Solution:
Factors of 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192
Factors of 196: 1, 2, 4, 7, 14, 28, 49, 98 and 196
So, the common factors of 192 and 196 are 1,2 and 4.
Hence, 196 and 192 have 3 common factors.
Example 2: 192 pieces of candy are to be divided equally among 5 children. The remaining pieces are to be placed in a jar. How many pieces will be placed in the jar?
Solution:
Number of pieces of candy = 192
Number of children = 5
Number of pieces of candy that each child receives = \(\frac{192}{5} \) = 38 R2
So each child receives 38 candies each. But after distributing the candies, 2 pieces of candy would be left behind, which would go into the jar.
Example 3: Chrisann has 192 marbles. She counts 16 marbles and labels them as group A, similarly for the next 16 she labels them as group B, she continues till she counts the last marble. What would the last group be labeled as?
Solution:
Number of marbles = 192
Number of groups of marbles = \(\frac{192}{16} \) = 12 R0
There are 12 groups of marbles. To find out what letter the last group would be labeled as, we need to count the 12th letter starting from A. The 12th letter is ‘L’.
Hence, the last group is labeled as group L.
Yes, 8 is a factor of 192. As 8 divides 192 exactly, that is, it leaves 0 as the remainder. So, 8 is a factor of 192.
Yes, 192 is a composite number as it has factors other than one and itself. It has factors of 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64 and 96 other than 1 and 192.
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192.
So, the least factor of 192 is 1 and the greatest factor is 192 itself.
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192.
Hence, the sum of all the factors of 192 is
= 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 = 508
Hence, the sum is 508.