Factors of 49 are basically the numbers that divide it evenly or exactly without leaving any remainder i.e if a number divides 49 with a remainder of zero, then that number is called a factor.
- All Factors: 1, 7 and 49
- Prime factors: 7
- Factors in pairs: (1, 49), (7, 7)
Prime Factorization of 49
Prime factorization is a method of “expressing” or finding the given number as the product of prime numbers. If a number occurs more than once in prime factorization, it is usually expressed in exponential form to make it more compact.
So, the Prime factorization here comes out to be: 7 × 7 = 72.
Prime Factorization of 49 by Upside-Down Division Method
Upside-Down Division is one of the techniques of Prime factorization used to factor numbers.
In this method, you will divide a given “composite” number evenly by the several prime numbers(starting from the smallest) till it gets a prime number.
It is called Upside-Down Division because the symbol is flipped upside down.
Here, 49 is an odd number. It is and only divisible by 7 and itself with no remainder. Thus, 7 is its smallest prime factor.
49÷ 7 = 7 Here, 7 is the prime number.
So we can stop the process.
Thus, Prime factorization with upside-down division method is: 7 × 7 = \(7^2 \).
Prime Factorization of 49 by Factor Tree Method
The Factor tree method is another technique for producing the prime factorization and all factors of a given number.
To use this method for a number x,
Firstly consider two factors say a,b of x such that a*b is equal to x and at least one of them (a, b) is a prime factor say a.
Then consider two factors of b say c, d such that again at least one of them is a prime factor. This process is repeated until both the factors are prime i.e if we get both the factors as prime at any step, we stop the process there.
Following is the factor tree of the given number.
Here we can get the prime factorisation of 49 as 7 * 7 and the prime factor is 7.
The sum of all the factors is 1 + 7 + 49 = 57
They have only one common factor which is 1 and that is why they can be called co-primes*.
Its pair factors are (1, 49), (7, 7). Pair factors of x are basically every pair of factors of x say (a,b) such that the product of a and b i.e a*b is equal to x.
*Coprimes: Two integers numbers, a and b, are said to be coprime numbers if their greatest common divisor is equal to one.