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Do perfect squares have an even or odd set of prime factors?
FactorsPerfect squares have an odd number of factors. If you think of factor pairs, the pair of factor that when multiplied together equals the given number, you realize that there are two factors for each pair until you come to the factor that when squared equals the number. For example, the factor pairs of 16 are 1 x 16, 2 x 8, and 4 x 4, giving us the factors of 1, 2, 4, 8, and 16 - an odd number of factors.Prime FactorsHowever, the situation is different with prime factors. It will depend on whether you list every prime factor or only the distinct prime factors. There will always be an even number of prime factors because when you square a number, you double the prime factors, which means you have an even number. That is not the case for distinct prime factors, because when you square a number, you are not adding any additional distinct factors. So, in some cases, there will be an even number of distinct prime factors and sometimes an odd number. Some examples follow.4 = 2 x 2. There are two prime factors, but one distinct prime factor.36 = 2 x 2 x 3 x 3. There are four prime factors and two distinct prime factors.900 = 2 x 2 x 3 x 3 x 5 x 5. There are six prime factors and three distinct prime factors.
How many factors does 36 have?
36 has 9 factors including 1 and 36. Its factors are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Which number has the most factors 6 17 25 or 36?
6 has 4 factors.17 has 2 factors.25 has 3 factors.36 has 9 factors ... 1, 2, 3, 4, 6, 9, 12, 18, and 36.I'll go with 36.
Which factors of 36 are perfect squares?
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. To determine which factors are perfect squares, we need to find the square root of each factor. The factors that have whole number square roots are perfect squares. In this case, the perfect squares among the factors of 36 are 1, 4, 9, and 36.
What is the smallest number that has both 4 and18 as factors?
36
