Factors of 64 are basically the numbers that divide it evenly or exactly without leaving any remainder i.e if a number divides 64 with a remainder of zero, then that number is called a factor.
- All Factors: 1, 2, 4, 8, 16, 32 and 64.
- Prime factors: 2.
- Factors in pairs: (1, 64), (2, 32), (4, 16), (8, 8).
Now, let us see the prime factors and prime factorization of the number.
Prime Factorization of 64
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.
- Prime factorization of 64 : 2 × 2 × 2 × 2 × 2 × 2 = 26.
Prime Factorization of 64 by Upside-Down Division Method
Upside-Down Division is one of the techniques of Prime factorization to find factors of any number.
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, 64 is an even number. So it is undoubtedly divisible by 2 with no remainder.
Thus we do 64÷ 2 = 32. Now find the prime factors of the obtained quotient.
Repeat Step 1 and Step 2 until we get a result of prime number as the quotient. Here, 32 is the quotient.
32÷ 2 = 16. Here, 16 is the quotient. Now find the prime factors of the 16.
16÷ 2= 8. Here, 8 is the quotient.
8÷ 2= 4. Here, 4 is the quotient.
4 ÷ 2= 2 Here, 2 is the prime number.
So we can stop the process.
So, now prime factorization of 64 with upside-down division method is: 2 × 2 × 2 × 2 × 2 × 2 and the only prime factor is 2.
Prime Factorization of 64 by Factor Tree Method
The Factor tree method is another technique for producing the prime factorization of a given number.
To use this method for a number x,
- Firsly 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 64 as 2 * 2 * 2 * 2 * 2 * 2 and the only prime factor is 2
1, 2, 4, 8, 16, 32 and 64 are the factors.
2 is the only prime factor.
Yes, 16 is a factor.