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How do you use the prime factorization of 72 to find all of its factors?
Wiki User
∙ 11y ago
The prime factorization of 72 is 2 x 2 x 2 x 3 x 3. That and the rules of divisibility tell us that 72 is divisible by 2, 3, 4, 6, 8 and 9. That should be enough information.
Write down the number and itself.
72 and 1 Divide 72 by 2
36 and 2 Divide 72 by 3
24 and 3 Divide 72 by 4
18 and 4 Divide 72 by 6
12 and 6 Divide 72 by 8
9 and 8
Answer:1,2,3,4,6,8,9,12,18,24,36,72
Wiki User
∙ 11y ago
Wiki User
∙ 11y agoFind the prime factorisation of 72 in power format.
Now multiply together all the primes for all the combinations of their powers from 0 to their maximum power which is the power of the factorisation. This is most easily done by:
- Write the primes all to the power 0
- Multiply the primes together to their relative powers (any prime to the power 0 is 1) to get the next factor
- Increase the power of the first prime by 1
- If this is not greater than its value in the prime factorisation, repeat from step 2.
- Reset the first prime's power to zero and increase the next prime's power by 1.
- If this is not greater than its value in its prime factorisation, repeat from step 2.
- Reset this prime to zero and increase the next prime's power by 1
- Keep repeating this until all the primes have gone through all their possible powers from 0 to their maximum value.
So for 72 this is:
72 = 23 x 32
⇒ its factors are:
20 x 30 = 1 x 1 = 1
21 x 30 = 2 x 1 = 2
22 x 30 = 4 x 1 = 4
23 x 30 = 8 x 1 = 8
20 x 31 = 1 x 3 = 3
21 x 31 = 2 x 3 = 6
22 x 31 = 4 x 3 = 12
23 x 31 = 8 x 3 = 24
20 x 32 = 1 x 9 = 9
21 x 32 = 2 x 9 = 18
22 x 32 = 4 x 9 = 36
23 x 32 = 8 x 9 = 72
So the factors of 72 are: 1, 2, 4, 8, 3, 6, 12, 24, 9, 18, 36, 72
Or in ascending order: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Wiki User
∙ 10y agoBy the rules of divisibility, you know that 72 is divisible by 1, 2, 3, 4, 6 and 8. Dividing those numbers into 72 gives you the other half.
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Wiki User
∙ 9y agoThe factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Wiki User
∙ 11y agoSince 36 is a factor of 72, all of its factors are included in the factors of 72. Just add 72 to the list of factors of 36.
Wiki User
∙ 9y agoThey are: 1 2 3 4 6 8 9 12 18 24 36 and 72
Wiki User
∙ 10y ago1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
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What is when the factors of the product are all prime?
That's a prime factorization.
What is the product of all of the prime factors?
That's the prime factorization.
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The idea is to divide numerator and denominator of a fraction by any common factors. Prime factorization is simply used to find all possible factors.
A number written as the product of all its prime factors is called?
A prime factorization
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That's finding the prime factorization.
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Prime factorization is when you find all the prime factors of a number.
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When all the factors are prime numbers, that's a prime factorization.
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All numbers have factors. Some factors are prime numbers, some are composite numbers, one is neither. When finding the factors of a number, you find all the factors. The prime factorization is a multiplication string of just prime factors that will total the given number.
What is the factorization in which all the factors are prime numbers of a number?
That's the prime factorization.
How do you know when you finish a prime factorization?
When all of the factors are prime.
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The prime factorization.
What is when the factors of the product are all prime?
That's a prime factorization.
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Find the prime factorization of each of the 13 numbers.Find the factors which appear in the prime factorization of all of the numbers.Multiply them together.
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The prime factorization.
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To find the prime factorization of a number, start with any factor pair of that number and keep factoring the composite numbers until all factors are prime. 55 5 x 11 = 55 Both factors are prime, so that is the prime factorization.
