A number factor — let’s call it N — is a numbers that can be multiplied by something to yield N as a product. Another way to put it is that the factors of a number are divisors of that number; that is, they can divide that number without leaving a remainder.
Let’s take examples of two numbers i.e., 21 and 54 to understand factors and how you can find factors of any composite number easily.
Factors of 21
Do you want to know what the factors of 21 are? Factors of 21 are all the integers, which are all the positive, negative, and whole numbers that can be evenly divided by 21. What’s astounding is that dividing 21 by a factor of 21 yields another factor of 21. These can thus be expressed as either individual or paired factors. In this scenario, we present them in both ways. Typically, this is a mathematical disintegration of a specific number.
Factors of 21 in Pairs
The factor pair of 21 is the pair of numbers that when multiplied together yields 32. The factor pairs of 21 are shown below.
1 × 21 = 21
3 × 7 = 21
7 × 3 = 21
21 × 1 = 21
- After 3 × 7, the factors begin to repeat.
- So, finding factors is sufficient until (3, 7)
- (1, 21) are two components of 21. (3, 7)
Prime Factorization of 21
A prime factorization is a result of factoring a number into a classification of components, each of which is a prime number. In textual form, this is commonly expressed by giving 21 as a product of its prime factors. This is the result for 21: 21 = 3 x 7. As a result, the total number of prime factors in a set of 21 is two.
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Factors of 54
Factors of 54 are numbers that can divide by 54 exactly. When two factors are multiplied together to yield the number 54, they form factor pairs.
We will use the pair factor and prime factorization methods to find the factors of an integer, 54.
Pair Factors of 54
The factor pairs of 54 are complete numbers, not fractions or decimal numbers.
To find the pair factors, multiply the two integers in a pair by 54 to get the original number.
1×54 = 54
2×27 = 54
3×18 = 54
6×9 = 54
As a result, the positive pair factors are (1, 54), (2, 27), (3, 18), (3, 18), (3, 18), and (6, 9).
Prime Factors of 54
54 is a composite number with a few prime factors. Let us now look at how to find the prime factors of 54.
To begin, divide 54 by the smallest prime component, say 2, to obtain 27. 54 2 = 27
Again, dividing 54 by 3 produces a fractional number that cannot be a prime factor, so move on to the next prime factor, say 3
27 ÷ 3 = 9
9 ÷ 3= 3
3 ÷ 3 =1
Finally, we get quotient 1 at the end of the prime factorization procedure. As a result, we have to stop. As a result, the prime factors of 54 are 2 × 3 × 3 × 3 or 2x 33, where 2 and 3 are the prime numbers.
Few Important Properties of Factors
- The factor of any given integer is its exact divisor.
- Every number has a factor of one.
- The factor must be less than or equal to the number at all times.
- A number’s greatest factor is the number itself.