All The Factors Of 87
In Maths, factors of 87 are the natural numbers that carve up the original number into equal parts. The product of two natural numbers results in 87, hence they get the factors of eighty-seven. 87 is an odd blended number, thus has more two factors.
Let us discover the factors of 87 along with pair factors and prime factors, using elementary division and prime number factorisation methods, respectively.
How to Discover Factors of 87?
The factor of 87 breaks the original number into equal numbers of parts. Therefore, at that place will be no remainder left later division. Let us see how to find the factors of the existent number 87.
87 ÷ 1 = 87 [Remainder = 0]
87 ÷ iii = 29 [Remainder = 0]
87 ÷ 29 = 3 [Remainder = 0]
87 ÷ 87 = 1 [Remainder = 0]
Thus, the factors of 87 are 1, 3, 29 and 87.
Pair Factors of 87
The pair factors of 87 are formed when two integers are multiplied together. Therefore, we can discover, there are just ii such pairs of numbers that can generate the original number, on multiplication.
one × 87 = 87
iii × 29 = 87
Therefore, the pair factors are (1, 87) and (3, 29).
At present, if nosotros consider the negative integers every bit a pair factors of 87, then we get;
-ane × -87 = 87
-3 × -29 = 87
As we can meet, from the to a higher place multiplication, two negative integers on multiplication with each other results in the original number. Therefore, the negative pair factors are (-one, -87) and (-3, -29).
Prime Factorisation of 87
By prime factorisation of 87, we can determine the prime numbers that can uniformly divide the original number. Thus, in this instance, nosotros will be dividing 87, just by the prime numbers.
Earlier we commencement evaluating the prime factors, allow us encounter what are the primes betwixt i and 87
List of prime number numbers (Between 1 and 87) :
2, 3, 5, 7, eleven, thirteen, 17, nineteen, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83
Follow the steps below to detect the prime factors.
Step 1: The smallest prime number by which 87 is divisible, is 3.
87/iii = 29
Pace two: Now, if nosotros see, from the list of primes, 29 itself is a prime number. Therefore, it is divisible by itself or ane. Since, i is non a prime number, therefore nosotros volition ignore it.
29/29 = i
Therefore, the prime factors of 87 are 3 and 29.
Prime factorisation of 87 = iii x 29
Exponential Form = 31 x 29ane
Video Lesson on Prime number Factors
Solved Examples
Q.one: Find the sum of all the factors of 87. Likewise, find if the sum is a prime number or composite number.
Solution: The factors of 87 are 1, three, 29 and 87 .
Sum = 1 + three + 29 + 87 = 120
Therefore, 120 is the required sum.
120 is a composite number, because it has more than two factors.
Factors of 120 are 1, 2, iii, 4, v, half dozen, eight, 10, 12, 15, 20, 24, thirty, forty, 60, 120.
Q.2: What is the greatest common gene of 90 and 87?
Answer: Permit us first write the factors of both the numbers.
Factors of 87 → 1, 3, 29, 87
Factors of 90 → ane, ii, 3, v, 6, 9, 10, 15, 18, thirty, 45, xc
Therefore, greatest common cistron (GCF) of 87 and 90 = 3
Q.3: What are the common factors of 85, 86 and 87?
Answer: The factors are:
85 → one, five, 17, 85
86 → one, 2, 43, 86
87 → 1, 2, 43, 87
Therefore, the common cistron is only 1.
Practise Problems
- Detect the average value of factors of 87.
- Find if 87 and 82 are co-prime numbers or not.
- John has 81 balls in the red basket and 87 balls in the blue basket. What is the maximum number of balls he tin distribute equally in each basket?
- What is the GCF of 81 and 87?
Register with united states and download BYJU'Due south – The Learning App to learn more well-nigh factors and prime factors with the aid of interactive videos.
Oftentimes Asked Questions on Factors of 87
What are the factors of 87?
In that location are a full of four factors of 87. These factors are 1, 3, 29 and 87.
What is the prime number gene grade of 87?
The prime factorisation of 87 is: 3 x 29.
Is 87 a prime? If non why?
87 is not a prime number but a composite number considering it exceeds the fact of having two factors.
What are the multiples of 87?
The showtime 10 multiples of 87 are 87, 174, 261, 348, 435, 522, 609, 696, 783 and 870.
Is 87 a perfect square?
87 is not a perfect square, because the square of no natural number results in 87.
All The Factors Of 87,
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