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Factors of 60 are those integers that on multiplication in pairs result in the number 60. It comprises the numbers that divide 60 exactly without leaving any remainder. These numbers are 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, which makes 60 a composite number. The factors are a set of numbers that results in the original number when multiplied together.
- 60 is the biggest factor and 2,3, and 5 are the prime factors of 60.
- It is easy to find the factors of a number with a simple multiplication method.
- The number 60 is a composite number, it has more than two factors.
Read more: Pair Factors & Prime Factors of 50
Key terms: Factor of 60, Prime factor, Prime factorization, Integers, Composite numbers, Negative factor, Remainder
What are the Factors of 60?
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The numbers multiplied in pair results in the number 60 are considered to be the factors of 60. That means the numbers that divide 60 exactly are the factors of 60. According to the definition of factors, the numbers that divide by 60 without leaving any reminder are the factors of 60. The factors of 60 are comprised of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. 60 also has negative factors such as -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30, and -60. So, when multiplying a negative factor with another negative factor (-30) × (-2) results in 60.
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How to Calculate the Factors of 60?
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Below given are the steps to find the factors of 60:
Step 1: The factors of 60 can be found easily through the method of multiplication.
To find the factors of the 60 using multiplication, we have to check what pairs of numbers have to multiply to get 60. We should start with the natural numbers.
Step 2: let’s take two numbers that on multiplication give 60, that is 1 and 60 as, 1×60= 60
Step 3: While taking 2, which is a prime number that results in 60 on multiplying, such as 2×30 = 60
We know that 2 is a prime number, which means the number with only two factors, 1 and the number itself
Step 4: In the same way we can continue with the natural numbers up to 9
3×20= 60
4×15= 60
5×12= 60
6×10= 60
So, the factors of 60 are 1,2,3,4,5,6,12,15,20,30, and 60.
Pair of Factors of 60
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Pair of 60 can be positive as well as negative numbers, but can not be decimal or fraction.
| Positive Pair Factors | |
|---|---|
| 1×60= 60 | (1,60) |
| 2×30 = 60 | (2,30) |
| 3×20= 60 | (3,20) |
| 4×15= 60 | (4,15) |
| 5×12= 60 | (5,12) |
| 6×10= 60 | (6,10) |
It is also possible to have negative pair factors as well because the product of two negative factors will be a positive number.
| Negative Pair Factors | |
|---|---|
| -1×-60= 60 | (-1, -60) |
| -2×-30 = 60 | (-2, -30) |
| -3×-20= 60 | (-3, -20) |
| -4×-15= 60 | (-4, -15) |
| -5×-12= 60 | (-5, -12) |
Prime Factorization of 60
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We can determine the prime factors of 60 with the method of prime factorization. We know 60 is a composite number. Let’s find the prime factors.
Step 1: 2 is the smallest prime factor. Let’s divide the number 60 by the prime number 2
60÷2= 30
Let’s check whether 30 can be further divided by 2 or not
30÷2= 15
As we know 15 is not divisible by 2 let’s take the next prime number which is 3
Step 2: Now divide 15 by 3 the results will be
15÷3= 5
If we divide 5 by 3 we get a fraction, it can’t be the factor. So, let’s take the next prime number 5
Step 3: While dividing 5 by 5,
5÷5= 1
The final result is one and we can’t further proceed with the process of division, as the multiple of So the prima factorization of 60 is 2×2×3×5 as it can also be written as 22 ×3×5, where 2,3, and 5 are prime numbers.
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Things to Remember
- As number 60 has factors other than number 1, 60 is considered to be a composite number
- Factors of 60 are considered to be the numbers that are completely divisible to 60 without leaving any remainder
- Decimals and fractions can’t be the factors
- Factors can be positive as well as negative numbers.
- Factors of 60 are
- Positive Factors: 1,2,3,4,5,6,10,12,15,20,30 and 60
- Negative Factors: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30 and -60
- Prime Factors of 60: 2,3,5
- Prime Factorization of 60: 2×2×3×5= 22×3×5= 60
Sample Questions
Ques. Find the common factors of 60 and 30. (2 marks)
Ans. The factors of 60 are 1,2,3,4,5,6,10,12,15,20,30,60
The factors of 30 are 1,2,3,5,6, 10,15 and 30
The common factors are 1,2,3,5,10,15, and 30
Ques. What is the product of all the distinct prime factors of 60? (2 marks)
Ans. Prime factors of 60 are 22×3×5= 60
Here we need distinct prime factors, therefore the product will be
2×3×5=30
Ques. Find the common factors between 60 and 25. (2 marks)
Ans. The factors of 60 are 1,2,3,4,5,6,10,12,15,20,30,60
The factors of 25 are 1,5, and 25
The common factors are 1 and 5
Ques. Find the factor pair of 60 in which one of the components of the pair is -15. (2 marks)
Ans. 60= factor 1×factor 2
60= (-15) ×factor 2
Therefore, factor 2= 60 ÷ -15= -4
Hence the pair will be= (-4) × (-15) = 60
Ques. Find the product of all prime factors of 60. (2 marks)
Ans. Prime factors of 60= 2,3, and 5.
Product of prime factors= 2×3×5=30
Ques. State True or False with respect to the factors of 60? (2 marks)
1. 2 and -3 are factors of 60
2. Only 2 and 5 are the factors of 60
Ans. a) True
- b) False
Ques. Find the common factors of 60 and 59. (2 marks)
Ans. Factors of 60= 1,2,3,4,5,6,10,12,15,20,30, and 60
Factors of 59= 1 and 59
Common Factor= 1
Ques. Find the sum of the positive factors of 60. (2 marks)
Ans. Sum of factors o 60= 1+2+3+4+5+6+10+12+15+20+30+60
= 168
Ques. What are the negative factors of 60? (2 marks)
Ans. -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30 and -60
Ques. What is the greatest common factor of 60 and 100? (2 marks)
Ans. Factors of 60= 1,2,3,4,5,6,10,12,15,20,30,60
Factors of 100= 1,2,4,5,10,20,25,50 and 100
Common Factors= 1,2,4,5,10,20
Hence the Greatest Common factor of 60 and 100= 20
Ques. What are the composite factors of 60? (2 marks)
Ans. 60 has 12 factors
1,2,3,4,5,6,10,12,15,20,30,60
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