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Factor trees are useful to see all of the factors of a number. If you end up with a composite, or un-Prime number, you havent successfully completed the factor tree.

for example:

50

10,5

you obviously wouldn't end here because you can break 10 down into 5 and 2

you finished tree would look like

50

10,5

5,5,2

Q: Why is it that whenever you use a factor tree you need to end up with a prime number?

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Two (or more) numbers are said to be co-prime if they have no prime factor in common. The numbers, themselves need not be prime. Thus, 14 (= 2*7) and 15 (= 3*5) are co-prime.

Prime numbers don't need trees.

A factor tree will show you the prime factorization of 88. Comparing that prime factorization of 88 and another number will you show you the GCF between the two. You need at least two numbers to find a GCF.

Divide the number by it's lowest prime factor possible continuosly until you get a one. The numbers will then be the prime factors. For example: Take the number 66. 2 is the smallest prime number and it is a factor of 64. So 66/2 = 33. 33 is not divisible by 2 so we take the next lowest prime factor: 33/3 = 11. 11 is divisible by nothing but itself and so 11 is the next lowest prime factor (remember we always need the answer to remain an integer): 11/11 = 1. Therefore 66 = 2 x 3 x 11.

You do not. To have a greatest common factor, you need two or more numbers. A common factor is a factor that two or more number have in common. However, the prime factorization of all the numbers will help you find the greatest common factor. The greatest common factor will be the prime factors they have in common multiplied together. Example: The prime factors of 45 are 3, 3, and 5. The prime factors of 60 are 2, 2, 3, and 5. The common prime factors are 3 and 5, so the greatest common factor is 3 x 5 = 15.

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You need to factor it, into prime factors. Then, for every prime factor that appears an ODD number of times, you need to multiply 2306 by this prime factor. Multiply all such prime factors together to get your answer.

37 is already prime. No need for a tree.

19 is already prime; no need for a tree.

No. If the number has one factor (other than 1 and itself) it is a composite. However, to establish that a number is prime it needs to be checked for divisibility by each prime number up to the square root of the number. If the only factor found is 1, then it is a prime.

13 is already prime. It doesn't need a tree.

GCF of a prime number and a composite number is 1 if the prime number is not a factor of the composite number. Here 103 is a prime number and 120 is a composite number. And 120 is not divisible by 103(or 103 is not a factor of 120). So, GCF(103,120) = 1

The prime factors of 110 are 2, 5 and 11. For them to be common, they need to be compared to another set of prime factors.

The prime factors of 6 are 2 and 3. For them to be common, they need to be compared to another set of prime factors.

All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this. Example: 210 210 Divide by two. 105,2 Divide by three. 35,3,2 Divide by five. 7,5,3,2 Stop. All the factors are prime. 2 x 3 x 5 x 7 = 210 That's the prime factorization of 210. The largest of those numbers is the largest prime factor.

To know that a number is prime you need to know that it has no factors other than 1 and the number itself.To know that a number is composite you only need to know one factor other than the number itself or 1.

A factor of a composite number need not be a prime number, some factors are themselves composite. Prime factorisation is continuing to factorise each factor unless it is a prime. For example, start with 30. 6 goes into 30 so finding a factor is satisfied by simply identifying 6 as a factor of 30. Now 30 = 5*6 where 5 is a prime, but 6 is not so we need to factorise 6. 6 = 2*3 and therefore, 30 = 5*2*3 = 2*3*5 The last is the prime factorisation of 30.

There is no easy way. You will have to try dividing it by the smallest prime (2), then the next one (3) and continue until you have tried out the all the primes up to and including the square root of the number. You do not need to find the quotient, you only need check for divisibility.