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The numbers that divide 68 to produce a quotient as a whole number are known as its factors. The original number is evenly divided by a number’s factor.
- The original number is obtained when one multiplies the factors of 68 in pairs.
- Unlike prime numbers, 68 is a composite number with more than two factors.
- 1, 2, 4, 17, 34, and 68 are the factors of 68.
- Since 68 is a composite number, it has more factors than just itself and 1.
- 1 is the smallest factor of 68, and 68 is the highest factor of 68.
Read More: Multiplication and Division
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Key Terms: Factors of 68, face value, variables, composite number, place value.
What are the Factors of 68?
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The numbers that can divide the starting number evenly are called factors of 68. Six variables make up the number 68: 1, 2, 4, 17, 34, and 68. These variables can each split 68 into an equal number of pieces.
- Since there are more than two factors, 68 is a composite number as a result.
- In this situation, the lowest and greatest factors are 1 and 68, respectively.
- A result, one has just assessed the two factors of 68.
- One can also organize the factors in ascending order after finding them.
- Factors of 68 are–
| Factors | Pair Factors | Prime Factors |
|---|---|---|
| 1, 2, 4, 17, 34, and 68 | (1, 68), (2, 34), and (4, 17) | 68 = 22 × 17 |
Read More: Natural numbers and Whole numbers
How to find Factors of 68?
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Factors are actual numbers that evenly or split the source number (in the case, 68). 1 is the factor of all whole numbers. A number itself can be considered a factor.
- 68 is an even number right now.
- It can therefore be divided by 2.
- As a result, the result of dividing 64 by 2 likewise has a factor of 68.
- Let’s look for every factor right now.
68 ÷ 1 = 68
68 ÷ 2 = 34
68 ÷ 4 = 17
68 ÷ 17 = 4
68 ÷ 34 = 2
68 ÷ 68 = 1
- Therefore, 1, 2, 4, 17, 34, and 68 are the factors of 68.
Read More: Integers
Factors of 68 by Prime Factorization
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Prime factorization is the process of breaking a composite number down into its prime components. One divides 68 by its smallest prime factor, 268 ÷ 2= 34, to obtain its prime factorization. By its smallest prime number, 2, 34 is now divided.
34 ÷ 2= 17
- Prime factorization is continued until the quotient equals 1.
- In light of this, the prime
- Factorization factors for 68 are:
Another way to write it is 68 = 2 × 2 × 17
One can multiply them to obtain the other factors now that one has completed the prime factorization of our number.
- One just needs two factors to make up factor pairs of 68; when these factors are added (multiplied), 68 results.
- The positive factor pairs of 68 are listed below:
1 × 68 = 68
2 × 34 = 68
4 × 17 = 68
17 × 4 = 68
34 × 2 = 68
68 × 1 = 68
- 68 can also contain negative factor numbers, as was already mentioned.
- A number can have drawbacks just like multiples do.
-1 × -68 = 68
-2 × -34 = 68
-4 × -17 = 68
-17 × -4 = 68
-34 × -2 = 68
-68 × -1 = 68
Read More: Quotient rule
All Factors of 68
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Now that one has all 68 factors, one can arrange them in any sequence to obtain.
68 > 34 > 17 > 4 > 1
One can deduce from this arrangement that the lowest and greatest factors of 68 are respectively 1 and 68.
Read More: Remainder Theorem
Factors of 68 in Ascending Order
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Since one already has all the relevant information for the number 68, let’s arrange the section in ascending order as follows:
1 < 2 < 4 < 17 < 34 < 68
The arrangement above shows that the smallest and greatest factors are 1 and 68, respectively.
Read More: Closure Property
Prime factorization of 68
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It is a composite number, the number 68. Let's now identify its main causes.
To get a fraction or an odd number, divide the number 68 by the smallest prime factor- in this case, 2, and then divide the result by 2 again.
68 ÷ 2 = 34
- Divide 34 again by 2, and the result is 17.
- As of right now, one is aware that 17 has only two variables, which are 1 and 17.
- As a result, one is unable to use the division method any further.
- Consequently, 2 and 17 are the prime factors of 64.
- 64’s prime factorization yields either 2 × 2 × 17 or 22 × 17.
Things to Remember
- The Factors of 68 are 1, 2, 4, 17, 34, and 68.
- The Sum of Factors 68 is 126.
- The Pair Factors of 68 are (1,68), (2,34), and (4,17).
- The Smallest factor of 68 is 1.
- The Highest factor of 68 is 68.
- The Prime Factors of 68 are 2 and 17.
- The Prime factorization of 68 is 22 × 17.
Sample Questions
Ques: What do we mean by factors of a number? (2 Marks)
Ans: A factor is a number that divides another number, without leaving a remainder.
Multiplying two whole numbers gives a product, the numbers we have multiplied are the factors of the product because they are divisible by the product.
Ques: How can we find the factors of a number? (2 Marks)
Ans: We can find the factors of a number by following the steps-
- Express the number as the product of its primes (prime factorization).
- Write the prime factorization of the number in the exponent form.
- Add 1 to every exponent.
- Multiply all the resultant numbers.
Ques: What is the sum of all factors of 68? (2 Marks)
Ans. The sum of all factors of 68 is explained below-
1+2+4+17+34+68=126.
Hence, the sum of all factors of 68 is 126.
Ques: Write the prime factorization of 68. (2 Marks)
Ans: Number 68 is composite, its prime factorization is -
- 68 ÷ 2 = 34
- 34 ÷ 2 = 17
Since 17 is a prime number, having only two factors, 1 and 17
So, 2 and 17 are the prime factors of 68.
Prime factorization of 68: 22 × 17 or 2 x 2 x 17
Ques: How can we find factors of 68? (2 Marks)
Ans: Since 68 is a composite number.
Dividing 68 by 2
68 ÷ 2 = 34
Again divide 34 by 2
34 ÷ 2 = 17
here 17 is a prime number, having only two factors, 1 and 17
Therefore, the Prime factors of 68 are 2 and 17.
Ques: List some important facts on factors of 68. (2 Marks)
Ans: Important facts on the factor of 68 are
- 1, 2, 4, 17, 34, and 68 are factors of 68
- Prime factorization of 68 is 22 × 17
- 2 and 17 are Prime factors of 68
- The Smallest factor of 68 is 1
- The Highest factor of 68 is 68
- The Sum of factors 68 is 126
- Pair of factors of 68 : (1,68), (2,34), and (4,17)
Ques: Write the factors of 68 in ascending order. (2 Marks)
Ans: The factors of 68 in ascending order are-
1<2<4<17<34<68
As per the arrangement, the smallest factor of 68 is 1 and the largest factor of 68 is 68.
Ques: How can we find factors of 68 in pairs? (2 Marks)
Ans: Multiply two numbers in a pair to get the original number, we can find the factors of 68 in pairs as mentioned below-
- 1 x 68 = 68
- 2 x 34 = 68
- 4 x 17 = 68
Here we get factors of 68 in pairs i.e.(1, 68), (2, 34), and (4, 17).
Ques: What are the properties of factors of a number? (2 Marks)
Ans: The properties of factors of a number are as mentioned below-
- Each natural number has a factor of itself.
- 1 is a factor of every number.
- A number’s factors are all less than or equal to the original value.
- Multiplication and division are two methods to find factors of a number.
- Except for 0 and 1, all whole numbers have at least two factors.
- Every number has a finite number of factors.
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