In Maths, factors of 192 are the natural numbers that divide the actual number, exactly. These factors are also called divisors. Since, 192 is a highly composite number, therefore the number of factors is more for 192. 192 is divisible by 2 since it is an even number. Also, the sum of all the digits of 192 is an even number, i.e., 12. Another interesting fact is that 192 is completely divisible by the sum of all the digits. (i.e) 192/12 = 16.
In this article, we are going to learn the pair factors and the prime factors of 192 with many solved examples.
Table of Contents:
- What are the Factors of 192?
- Pair Factors of 192
- How to Find the Factors of 192?
- Prime Factorisation of 192
- Solved Examples
- Practice Questions
- FAQs
What are the Factors of 192?
The factors of 192 are the numbers that divide the number 192 exactly without leaving any remainder. As the number 192 is a composite number, it has many factors other than 1 and 192. Thus, the factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192. Similarly, the negative factors of 192 are -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96 and -192.
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Factors of 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192. Prime factorisation of 192: 2 × 2 × 2 × 2 × 2 × 2 × 3 or 26× 3 |
Pair Factors of 192
If the product of two natural numbers is equal to 192, then such pairs of numbers are called pair factors of the original number.
- 1 × 192 = 192
- 2 × 96 = 192
- 3 × 64 = 192
- 4 × 48 = 192
- 6 × 32 = 192
- 8 × 24 = 192
- 12 × 16 = 192
Therefore, the positive pair factors of 192 are (1, 192), (2, 96), (3, 64), (4, 48), (6, 32), (8, 24), (12, 16).
Pair factors can be considered with a negative sign, since the product will result in a positive number.
- -1 × -192 = 192
- -2 × -96 = 192
- -3 × -64 = 192
- -4 × -48 = 192
- -6 × -32 = 192
- -8 × -24 = 192
- -12 × -16 = 192
Therefore, the negative pair factors are (-1, -192), (-2, -96), (-3, -64), (-4, -48), (-6, -32), (-8, -24), (-12, -16).
How to Find the Factors of 192?
The factors of 192 can be determined by checking with what numbers, the actual number is completely divisible. It means that the remainder should remain zero.
- 192 ÷ 1 = 192
- 192 ÷ 2 = 96
- 192 ÷ 3 = 64
- 192 ÷ 4 = 48
- 192 ÷ 6 = 32
- 192 ÷ 8 = 24
- 192 ÷ 12 = 16
- 192 ÷ 16 = 12
- 192 ÷ 24 = 8
- 192 ÷ 32 = 6
- 192 ÷ 48 = 4
- 192 ÷ 64 = 3
- 192 ÷ 96 = 2
- 192 ÷ 192 = 1
Therefore, we can conclude the factors of 192, i.e., 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. There are a total 14 factors, including 1 and the number itself.
More Factors
Prime Factorisation of 192
Prime factorisation of 192 is equal to the product of prime factors. This method will yield the prime factors of the actual number, by which it is divisible.
| Dividing 192 by smallest prime number, i.e.2 | 192 ÷ 2 = 96 |
| 96 is again divisible by 2 | 96 ÷ 2 = 48 |
| 48 is also divisible by 2 | 48 ÷ 2 = 24 |
| 24 is an even number and divisible by 2 | 24 ÷ 2 = 12 |
| 12 divided by 2 | 12 ÷ 2 = 6 |
| 6 divided by 2 | 6 ÷ 2 = 3 |
| Now, 3 is itself a prime number. | 3 ÷ 3 = 1 |
Therefore, the prime factors of 192 are 2 and 3.
Therefore, the Prime factorisation of 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 or 26 × 3.
Video Lesson on Prime Factors
Solved Examples
Q.1: What is the value of 192 divided by 32?
Solution: 192 divided by 32 is:
192 ÷ 32 = 6
Therefore, the value of 192 divided by 32 is 6.
Q.2: What is the sum of all factors of 192?
Solution: The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192.
Sum of all factors = 1 + 2 + 3 + 4 + 6 + 8 +12 +16 + 24 + 32 + 48 + 64 + 96 + 192
= 508
Q.3: What is the greatest common factor of 192 and 200?
Solution: We can find the GCF or greatest common factor using the listing the factors method.
192 → 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
200 → 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Therefore, the GCF of 192 and 200 is 8.
Q.4: Find the common factors of 216, 288 and 192.
Solution: To find the common factors of the given numbers, we need to list down the factors.
Factors of 192 → 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
Factors of 216 → 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
Factors of 288 → 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
Therefore, the common factors are 1, 2, 3, 4, 6, 8, 12, 24
Practice Questions
- How many factors are there for number 192?
- How can we divide 192 into 24 equal parts?
- Smita wants to arrange 192 pages in a folder having 16 slots. How many pages can she keep in each slot of the folder.
- What is the GCF of 192 and 220?
- What are the factors of 192 that are not odd numbers?
Register with us and download BYJU’S – The Learning App to learn more about factors and prime factors with the help of interactive videos.
Frequently Asked Questions on Factors of 192
What are the factors of 192?
The 14 factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
What is the prime factor form of 192?
The prime factor form of 192 is 2 x 2 x 2 x 2 x 2 x 2 x 3 or 26 x 3.
Is 192 a perfect square?
192 is not a perfect square. The square root of 192 is not a whole number but an irrational number.
What is the GCF of 192 and 198?
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192 and factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198. Therefore, the GCF of 192 and 198 is 6.
What is the highest factor of 192 apart from itself?
The highest factor of 192 apart from itself is 96.
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