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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.

Q: How do you break down each number into a prime factors?

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To find the factors of a number you should first break that number down into its prime factors. In this case 65 can be broken down as: 65 = 5x13 To find any other factors, you then multiply any combination of these prime factors together. In this case, the factors of 65 come out as: 1, 5, 13 and 65.

Once you break a number down to prime factors, you can group together the factors that are the same. For example,... 200 = 2 * 2 * 2 * 5 * 5 = 23 * 52

The first step to finding the factors of a number is to break the number down into its prime factors. In this case, 66 can be broken down as follows: 66 = 2x3x11 To find the other factors (apart from one) you have to multiply any combination of these prime factors together. That gives us the factors of 66 as: 1, 2, 3, 6, 11, 22, 33, 66.

The best way to break down a number (from the perspective of arithmetic!) is to write it as a product of its prime factors. For instance, 24 = 2 x 3 x 4 where x is the multiplication operator and of course 2, 3, and 4 are all prime numbers.

A number is relatively prime to a number if it has no common prime factors with that number. To calculate relative primes, we need to break 170 down into its prime factors. These are: 2, 5, 17. Thus we want to find a number that is made up solely from multiplying 3s, 7s, 11s, 13s, 19s, 23s, 29s and 31s together. The largest number less than 100 that meets this criteria is 99, which has prime factors of 3, 3 and 11.

Related questions

No, 11 is a prime number, you cannot break it into factors.

That's two words and it means to break down a composite number into the product of its prime factors.

The first step in identifying factors would be to break a number down into its prime factors. In this case, the number 67 is already prime, so cannot be broken down any further. Thus, the only factors of 67 are 1 and 67. The factors of any prime number are always just 1 and itself.

A prime number is when a number can be divided by 1 and itself; has only two factors. 1 is not a prime numberbecause it can only be divided by one. Not only that, but it also has to break down a composite number. When you divide a number by 1, it does not break down. It only stays the same.

To find the factors of a number you should first break that number down into its prime factors. In this case 65 can be broken down as: 65 = 5x13 To find any other factors, you then multiply any combination of these prime factors together. In this case, the factors of 65 come out as: 1, 5, 13 and 65.

11 is already prime.

Once you break a number down to prime factors, you can group together the factors that are the same. For example,... 200 = 2 * 2 * 2 * 5 * 5 = 23 * 52

The first step to finding the factors of a number is to break the number down into its prime factors. In this case, 66 can be broken down as follows: 66 = 2x3x11 To find the other factors (apart from one) you have to multiply any combination of these prime factors together. That gives us the factors of 66 as: 1, 2, 3, 6, 11, 22, 33, 66.

factoring

The breaking down of a composite number into its prime number factors.

List the number at the bottom. Break it down into factors by placing them on successive lines above the original number. Stop when all the factors are prime. 7,5,3,2 35,3,2 105,2 210

The first step in finding the factors of a number is to break it down into its prime factors. 55 is known from times tables to be 5x11, so we know its prime factorization is 5x11. To find any factors other than 1, you just multiply any combination of the prime factors together. In this case, 55 gives us the factors of: 1, 5, 11 and 55.