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Factors of 45 are the numbers that, when multiplied in pairs, result in the original number 45. The numbers that divide 45 evenly completely are the factors of 45. 45 has a total of six factors which are 1, 3, 5, 9, 15, and 45. The number 45 has only two prime factors which are 3 and 5. Pair factors of 45 are the numbers that give the product as 45 on multiplication with each other. The pair factors of 45 are (1, 45), (3, 15), and (5, 9).
- Factors of 45: 1, 3, 5, 9, 15, 45
- Prime Factors of 45: 3, 5
- Prime Factorization of 45: 3 × 3 × 5 = 32 × 5
Key Terms: Factors of 45, Factor Pairs, Prime Factorization, Pair Factors, Remainder, Prime Factors, Prime Numbers, Multiplication
What are Factors of 45?
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Factors of 45 are the natural numbers that divide the original number 45 completely. When 45 is divided by any of its factors, no remainder is left at the end of the division process. 45 is a composite number and thus has more than two factors. There are a total of six factors of 45 which are 1, 3, 5, 9, 15, and 45.
| Factors of 45 = 1, 3, 5, 9, 15, 45 |
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How to Calculate Factors of 45?
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Factors are the numbers that divide a given number completely, or the quotient obtained is a whole number. In simpler words, if the given number is completely divisible by a natural number, then that number is the factor of the given number.
To find the factors of 45 by the division method, we need to divide 45 by the natural numbers from 1 to the number 45. If the remainder is zero at the end of the division, then that number is a factor of 45.
- 45 ÷ 1 = 45 × 1 + 0 (Remainder = 0; 1 and 45 are factors)
- 45 ÷ 2 = 22 × 2 + 1 (Remainder ≠ 0; 2 and 22 are not factors)
- 45 ÷ 3 = 15 × 3 + 0 (Remainder = 0; 3 and 15 are factors)
- 45 ÷ 4 = 11 × 4 + 1 (Remainder ≠ 0; 2 and 22 are not factors)
- 45 ÷ 5 = 9 × 5 + 0 (Remainder = 0; 5 and 9 are factors)
- 45 ÷ 6 = 7 × 6 + 3 (Remainder ≠ 0; 7 and 6 are not factors)
- 45 ÷ 7 = 6 × 7 + 3 (Remainder ≠ 0; 6 and 7 are not factors)
Thus, the factors of 45 are 1, 3, 5, 9, 15 and 45. Any other number other than these would result in a remainder at the end of the division process, and thus, cannot be classified as the factors of 45.
Read More: HCF of Two Numbers
Prime Factorization of 45
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45 is a composite number, thus, the prime factors of 45 can be found through the prime factorization of 45. The step-by-step procedure for the prime factorization of 45 is as follows:
Divide the number 45 with the smallest prime factor 2.
45 ÷ 2 = 22.5
A fraction is obtained as the quotient, thus, we will move on to the next prime number, i.e. 3.
45 ÷ 3 = 15
15 ÷ 3 = 5
Now, if we divide 5 by 3, we will again get a fraction. Thus, we will move on to the next prime number which is 5.
5 ÷ 5 = 1
We have received 1 at the last of the division process, which means the further division is not possible. Thus, the prime factorization of 45 is 3 × 3 × 5 or 32 × 5 with 3 and 5 being the two prime factors of 45.
Read More: Prime Number Formula
Factor Tree of 45
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Factors of 45 can also be expressed with the help of a factor tree. A factor tree is a graphical presentation of the factors of a number with its prime factors at the end of each branch.
Factor Tree of 45 is as follows:
Factors of 45 in Pairs
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Pair factors of 45 are a set of two numbers that result in the number 45 when multiplied together.
The positive pair factors of 45 are (1, 45), (3, 15), and (5, 9).
- 1 × 45 = 45
- 3 × 15 = 45
- 5 × 9 = 45
The negative pair factors of 45 are (-1, -45), (-3, -15), and (-5, -9).
- -1 × -45 = 45
- -3 × -15 = 45
- -5 × -9 = 45
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Things to Remember
- Factors of 45 are the numbers that divide 45 uniformly leaving zero as the remainder.
- 1, 3, 5, 9, 15, and 45 are the factors of 45.
- (1, 45), (3, 15), and (5, 9) are the three pair factors of 45.
- The prime factorization of 45 is 3 × 3 × 5.
- 3 and 5 are the two prime factors of 45.
- The sum of all the factors of 45 is 78.
Sample Questions
Ques. What are the Factors of 45? (2 Marks)
Ans. Factors of 45 are the numbers that divide 45 completely and leave zero as the remainder at the end of the division process, The factors of 45 are 1, 3, 5, 9, 15, and 45. They can be expressed as:
- 1 × 45 = 45
- 3 × 15 = 45
- 5 × 9 = 45
Ques. Find the Greatest Common Factor of 45 and 40. (2 Marks)
Ans. The factors of 45 and 40 are
- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The common factors of 45 and 40 are 1 and 5, thus, the greatest common factor of 45 and 40 is 5.
Ques. Find all the factors of 45 by the prime factorization method. (3 Marks)
Ans. We need to find the factors of 45 by prime factorization
We know that
45 = 15 × 3 ……(i)
45 = 9 × 5 …….(ii)
From (i) and (ii), we can clearly obtain the two prime factors of 45, i.e. 3 and 5.
Therefore, 45 can be written as
45 = 3 × 3 × 5 .…..(iii)
Also, for finding all the factors of 45, we can multiply the prime factors of 45, i.e. 3, 3, and 5 from (iii) with each other to obtain other factors.
3 × 3 = 9 …….(iv)
3 × 5 = 15 ……..(v)
3 × 3 × 5 = 45 ……..(vi)
From the above equations (iv), (v), and (vi), we get the factors of 45 as 1, 3, 5, 9, 15, and 45.
Ques. Is 45 a prime number? (2 Marks)
Ans. No, 45 is not a prime number, because it has factors other than 1 and itself which are 3, 5, 9, and 15. Thus, 45 is a composite number as it has more than two factors apart from 1 and itself. The factors of 45 are 1, 3, 5, 9, 15, and 45.
Ques. What is the difference between prime factors and factors of 45? (2 Marks)
The prime factors of 45 are 3, and 5, whereas the total factors of 45 are 1, 3, 5, 9, 15, and 45.
Ques. What is factor tree 45? (2 Marks)
Ans. The factor tree of a given number is a pattern that represents all the factors of a given number in such a way that the multiplication of those factors results in the given number itself. The factor tree only includes prime factors. The factor tree of 45 is as follows:
Ques. What are the negative factors of 45? (1 Mark)
Ans. The negative factors of 45 are the factors that leave the remainder zero, but the quotient of divisibility is a negative integer. The negative factors of 45 are -1, -3, -5, -9, -15, and -45.
Ques. What are the multiples of 45? (2 Marks)
Ans. Multiples of 45 are the numbers that are produced when 45 is multiplied by any other natural number. The first 10 multiples of 45 are given as follows:
- 45 × 1 = 45
- 45 × 2 = 90
- 45 × 3 = 135
- 45 × 4 = 180
- 45 × 5 = 225
- 45 × 6 = 270
- 45 × 7 = 315
- 45 × 8 = 360
- 45 × 9 = 405
- 45 × 10 = 450
Ques. State the numbers which are a factor of 45 and also a multiple of 3. (1 Mark)
Ans. The numbers which are the factors of 45 as well as the multiples of 3 are 9, 15, and 45.
Ques. Find the sum of all the factors of 45. (2 Marks)
Ans. We know that the factors of 45 are 1, 3, 5, 9, 15, and 45. Adding up all these factors, we get
1 + 3 + 5 + 9 + 15 + 45 = 78
Thus, the sum of all the factors of 45 is 78.
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