Factors of 68
Introduction
Understanding the factors of 68 is crucial for various mathematical problems. Factors are numbers that divide 68 completely without leaving a remainder. In this guide, we will explore the factors of 68, how to find them, and their significance in various mathematical contexts.
Also Check: Cube root table
Factors of 68
Factors are numbers that divide 68 exactly. For 68, these numbers are 1, 2, 4, 17, 34, and 68. Since 68 can be divided by these numbers without leaving a remainder, they are considered its factors.
| Factors of 68 |
|---|
| 1 |
| 2 |
| 4 |
| 17 |
| 34 |
| 68 |
How to Find Factors of 68
To find the factors of 68, we need to identify numbers that can divide 68 without leaving a remainder. Here’s a simple method:
- Divide 68 by the smallest whole number (1).
- Continue dividing by subsequent whole numbers to see if the quotient is also a whole number.
- Repeat this process until you have found all factors.
Also Check: Differential Equations
Here are the steps:
- 68÷1=68
- 68÷2=34
- 68÷4=17
- 68÷17=4
- 68÷34=2
- 68÷68=1
Thus, the factors of 68 are 1, 2, 4, 17, 34, and 68.
Factors of 68 in Pairs
Factors can also be found in pairs. Pair factors of 68 are numbers that, when multiplied together, equal 68. Here are the pairs:
| Pair Factors of 68 |
|---|
| 1 and 68 |
| 2 and 34 |
| 4 and 17 |
Negative pair factors are also valid as multiplying two negative numbers results in a positive product:
- −1×−68=68
- −2×−34=68-
- −4×−17=68
Also Check: Cubes from 1 to 50
Factors of 68 in Ascending Order
When we arrange the factors of 68 in ascending order, we get:
| Factors of 68 in Ascending Order |
|---|
| 1 |
| 2 |
| 4 |
| 17 |
| 34 |
| 68 |
Prime Factorization of 68
Prime factorization involves breaking down 68 into its prime factors. Here's how it's done:
- Divide 68 by the smallest prime number, which is 2: 68÷2=34
- Divide 34 by 2: 34÷2=17
- 17 is a prime number, so it cannot be divided further.
Thus, the prime factorization of 68 is 2×2×17or 22×17
Also Check: Discontinuity
Examples
-
Sum of All Factors of 68
- The factors of 68 are 1, 2, 4, 17, 34, and 68.
- Sum = 1+2+4+17+34+68=126
-
Greatest Common Factor (GCF) of 60 and 68
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 68: 1, 2, 4, 17, 34, 68
- Common factors: 1, 2, 4
- Greatest Common Factor: 4
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Frequently Asked Questions on Factors of 68
No, 68 is not a prime number; it is a composite number because it has more than two factors.
The number 68 is written as "sixty-eight" in words. It is a natural number in mathematics, representing a specific value or quantity.
The number 68 has six factors: 1, 2, 4, 17, 34, and 68. Since it has more than two factors, it is classified as a composite number.
The factors of 68 are 1, 2, 4, 17, 34, and 68.