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There are a few ways to go about factoring. You can decide what works best for you. I always find the prime factorization first. Let's look at a random number: 108
The prime factorization can be found by using a factor tree.
108
54,2
27,2,2
9,3,2,2
3,3,3,2,2
2^2 x 3^3 = 108
Half of the factors will be less than the square root, half greater. If the number is a perfect square, there will be an equal number of factors on either side of the square root. In this case, the square root is between 10 and 11.
Adding one to the exponents of the prime factorization and multiplying them will tell you how many factors there are. In this case, the exponents are 2 and 3. Add one to each. 3 x 4 = 12
108 has 12 factors. Six of them are 10 or less, six of them are 11 or greater. All we have to do is divide the numbers one through ten into 108. If the result (quotient) turns out to be an integer, you've found a factor pair. Knowing the rules of divisibility will make that even easier.
108 is divisible by...
1 because everything is.
2 because it's even.
3 because its digits add up to a multiple of 3.
4 because its last two digits are a multiple of 4.
6 because it's a multiple of 2 and 3.
9 because its digits add up to a multiple of 9.
That's six factors less than 10. Divide them into 108. That's the rest of them.
(108,1)(54,2)(36,3)(27,4)(18,6)(12,9)
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Notice that all of those numbers, except 1, can also be found in the prime factorization.
Multiples are found by multiplying your number by successive counting numbers.
108 x 1 = 108
108 x 2 = 216
108 x 3 = 324
And so on forever. Since numbers don't stop, multiples don't stop either.
Using the commutative and associative properties of multiplication it is sometimes possible to simply the multiplication.
For example, to multiply 35 by 6,
35 = 5*7
6 = 2*3
therefore, 35*6 = (5*7)*(2*3) use the associative property
= 5*7*2*3 use the commutative property for the middle two terms
= 5*2*7*3 use the associative property for the first two terms, and for the other two terms.
= (5*2)*(7*3) = 10*21 = 210.
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What times what equal 285?
To find two numbers that multiply to 285, you can factorize 285 into its prime factors: 3 x 5 x 19. These prime factors can be combined in different ways to form pairs of numbers that multiply to 285. So, the pairs of numbers that multiply to 285 are 3 and 95, 5 and 57, or 15 and 19.
What are numerical factors?
Factors are numbers that multiply to create products. 2 x 3 = 6. Two and three are factors of six. Six is the product of two and three.
Will you get the same number of factors if you multiply a prime number and itself?
Prime numbers have two factors. Prime squares have three factors. Square numbers have an odd number of factors but that number varies.
When you multiply two whole numbers the product is equal to or greater than either of the factors is this true or false?
False.
When can you multiply two numbers together to get the least common multiple?
When they have no common prime factors.
What is more than two ways to multiply two factors of 144?
to multiply more than two factors for 144 are 12212 144
What are all the ways to multiply with more than two factors that equal 60?
1x30x2
How to multiply with more than 2 factors?
ways to multiply 90 more than 2 factors
How do you figure out ways to multiply with three or more factors?
1. Pick any two factors. 2. Multiply them. 3. Take the result and any left-over factor. 4. Multiply them. Repeat step 3 and 4 till you run out of factors.
Ways to multiply with two factors of 50?
1 x 50 2 x 25 5 x 10
What are all the ways to multiply 140 with 3 factors?
Hi
When you multiply two numbers what do you call the two numbers that you multiply?
The two (or more) numbers that you multiply are called factors. (The result of the multiplication is called the product.)
How do you know a number if its factors are given?
There are two ways in which the factors can be given. You are given all the prime factors (and their multiplicity). In that case simply multiply them all together. Or You are given each factor. In this case, the biggest of these is the number.
The number you get when you multiply two factors?
A product.
What are all ways to multiply with 2 factors to make the product of 144?
1x144,2x72
What are all ways to multiply and get 21?
1 21 7 3 are the factors
How can you multiply with more than two factors?
To multiply with more than two factors, you can use at least three numbers that it would take to multiply to get the larger number. For example, the number 50, with two factors can be 1X50, 2X25, or 5X10. But if you are asked for more than two factors, you could do this: 2X5X5 Factor 72 using more than two factors: 2X2X2X3X3
