When expressing a number as a product of its prime factors as for example 2*2*2*2*2*2 = 64
The product of all of the factors of 12 is 1,728 .
22 x 52 x 19 = 1900
The product of all factors of the two numbers is 2097152.
No. Any number of positive factors will lead to a positive product.
Power
The Product will be Repeat..like they say it is a Repeated Addition
a-n = 1/an = (1/a) x .... x (1/a), this last product having n factors, each is 1/a
18 has square factors, but no repeated ones.
The repeated factor of 102 is 10.
When expressing a number as a product of its prime factors as for example 2*2*2*2*2*2 = 64
how can exponent can make it easier to write an expression with a repeated factor in the product
Numbers can be expresed in terms of their prime factors as for example:- As a product of its prime factors: 3*31*73 = 6789
Exponents are a short way to count the repeated factors. 2 x 2 x 2 x 3 x 3 = 72 23 x 32 = 72
Exponents count the number of repeated factors. 2 x 2 x 2 x 3 x 3 = 72 2^3 x 3^2 = 72
The expression 2x3x4x5 can be simplified to 120. The number 120 has the least number of factors because it is a product of consecutive prime numbers (2, 3, and 5). When a number is a product of distinct prime numbers, it will have fewer factors compared to numbers with repeated prime factors. In this case, 120 only has 16 factors, making it the least among numbers with the same number of prime factors.
As a product of its prime factors in exponents it is: 22*52 = 100