Factors of 55

In Mathematics, factors of 55 are the numbers that divide the original number, evenly or uniformly. Since 55 is a composite number, it has more than two factors. These factors can be determined by the simple division method. After division we need to check if any remainder is left or not. If remainder is zero, then the divisor is the factor.

Apart from the factors we are going to determine here prime factors and pair factors of 55. These prime factors are nothing but the prime numbers and pair factors result in the original number when multiplied in pair with each other.

Factors Pair Factors Prime Factors
1, 5, 11 and 55 (1, 55) and (5, 11) 55 = 5 x 11

How to Find Factors of 55?

Factors are the integers that divide the original number (in this case, 55), completely. It means, there is no remainder left, after division and quotient is a whole number.

55 ÷ 1 = 55

55 ÷ 5 = 11

55 ÷ 11 = 5

55 ÷ 55 = 1

In all the above four divisions we can see, the remainders are zero and quotients are not a fraction. Thus, the factors of 55 are 1, 5, 11 and 55.

Pair Factors of 55

Pair factors are the numbers that result in the original number (in this case 55) when we multiply them or find the product of factors in pairs. Here, 1 and 55 makes a pair and 5 and 11 makes another pair, such that;

1 × 55 = 55

5 × 11 = 55

Therefore, the pair factors are (1, 55) and (5, 11).

Now, if we consider the negative pair factors, then the multiplication of negative numbers will result in a positive number. Thus,

-1 × -55 = 55

-5 × -11 = 55

Therefore, the negative pair factors are (-1, -55) and (-5, -11).

Prime Factorisation of 55

Prime factors of 55 are the primes that can divide the original number into equal number of parts. The list of prime numbers from 1 to 55 is given below to figure out the prime factors.

List of prime numbers (1 to 50) :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53

Step 1: From the above list, we can conclude 55 is completely divisible by 5. Thus, the smallest prime factor for 55 is 5.

55/5 = 11

Step 2: Now, 11 itself is a prime number, thus it is divisible either by 1 or itself.

11/11 = 1

We cannot divide further since the dividend is equal to 1 and it is divisible by 1 only.

Therefore,

Prime factorisation of 55 = 5 x 11

Solved Examples

Q.1: If 5 notebooks are bought by Sam for Rs. 55. Then what is the cost of each notebook?

Solution: Given,

Number of notebooks bought = 5

Cost of 5 notebooks = Rs. 55

Cost of each notebook = 55/5 = 11

Therefore, each notebook will cost Rs. 11.

Q.2: Find the sum of all the factors of 55. Also, find the average.

Solution: The factors of 55 are 1, 5, 11 and 55.

Sum = 1 + 5 + 11 + 55 = 72

Therefore, 72 is the required sum.

Now, we need to find the average of the given factors.

Since, Average = (Sum of all values)/Total number of values

Hence,

Average = 72/4 = 18

Thus, 18 is the required average.

Q.3: What are the common factors of 45 and 55?

Answer: Let us write first, the factors of both the numbers.

55 → 1, 5, 11, 55

45 → 1, 3, 5, 9, 15, 45

Hence, the common factors are 1 and 5.

Q.4: What is the GCF of 55 and 60?

Solution: Let us list down the factors of all the given numbers.

The factors of 55 are: 1, 5, 11, 55

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 75 are: 1, 3, 5, 15, 25, 75

Therefore, GCF of 55, 60 and 75 is 5

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Frequently Asked Questions on Factors of 55

What are the factors of 55?

There are a total of four factors of 55. These factors are 1, 5, 11 and 55.

What is 55 as a product of prime factors?

The prime factorisation of 55 is:

55 = 5 x 11

Where 5 and 11 are the prime numbers.

What are the multiples of 55?

The first ten multiples of 55 are 55, 110, 165, 220, 275, 330, 385, 440, 495 and 550

Is 3 a factor of 55?

No, 3 is not a factor of 55 because 55 divided by 3 is not a whole number.

55/3 = 18 [Remainder = 1]

Is 55 a prime number?

No, 55 is a composite number because it has more than 2 factors.

Is 55 a perfect square?

No, 55 is not a perfect square because the root of 55 will not result in a whole number.

√55 = 7.416 (approx)

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