The quickest way to find the factors of a number is to divide it by the smallest prime number (bigger than 1) that goes into it evenly with no remainder. Continue this process with each number you get, until you reach 1.
For a number N, whose prime factorization is Xa × Yb, we get the total number of factors by adding 1 to each exponent and then multiplying these together. This expresses the number of factors formula as, (a + 1) × (b + 1), where a, and b are the exponents obtained after the prime factorization of the given number.
Best Approach: If you go through number theory, you will find an efficient way to find the number of factors. If we take a number, say in this case 30, then the prime factors of 30 will be 2, 3, 5 with count of each of these being 1 time, so total number of factors of 30 will be (1+1)*(1+1)*(1+1) = 8.
One guideline for choosing the number of factors is to check eigenvalues of the correlation matrix. A common recommendation is to select the number of factors to be equal to the number of eigenvalues greater than or equal to one (Kaiser, 1960).
∴176 has greatest number of factors. Was this answer helpful?
Finding the factors of the fractions is the same as finding the factors of a whole number. For example: In the fraction , factors of 3 are 1, 3 and factors of 5 are 1, 5. So, the factors of are 1, 3, , . So, the factor pairs of are (1, ; (3, ).
The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number. 18 and 24 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.
The simplest algorithm to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, prime factorizing the number 30 we get, 30/2 = 15, 15/3 = 5, 5/5 = 1. Since we received the remainder, it cannot be further factorized.
A multiple of a number is a number that is the product of a given number and some other natural number. For example, when we multiply 7 by 3, we get 21, i.e. 7 × 3 = 21. Here, 21 is the multiple of 7.
Factors are the numbers which divide the given number exactly, whereas the multiples are the numbers which are multiplied by the other number to get specific numbers. It is time to recollect, to understand the concept of multiples and factors of a number.
Sanika found the smallest number with exactly 100 factors: Prime factorising 100 gives us 2\times2\times5\times5, now we can assign the smallest prime bases to the largest powers, which will give us 24$\times34\times5\times7 = 45360.
Therefore, 1 is a factor of every number and every number is a factor of itself.
144 is the smallest number that has exactly 15 factors.
The best method for teaching students how to find factor pairs is to have them start at 1 and work their way up. Give your students a target number and ask them to put “1 x” below it. Let them fill in the right side with the number itself. We know that any number has one “factor pair” of 1 times itself.
factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
Step 1 of solving this GRE question : Find the smallest positive integer that has 7 factors. The number of factors of number N is 7. 7 is a prime number. So, any number that has 7 factors will have p = 0 and q = 6.