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What prime numbers can divide 30 exactly?

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What prime numbers can divide 30 exactly?

The prime factors of 30 are the numbers 2, 3, and 5.

Why is it that if P is a prime number bigger than 3 then p2 1 is always divisible by 24 with no remainder?

Therefore since either p-1 or p+1 is divisible by 4 and the other 2, their product is divisible by 8. But it was also established previously that (p-1)(p+1) is divisible by 3. Therefore (p-1)(p+1) is divisible by 8 and 3, and therefore 24. This means for any prime p > 3, p^2 – 1 = (p-1)(p+1) is divisible by 24.

How do you find the factor of 30?

Factors of 30

  1. Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30.
  2. Negative Factors of 30: -1, -2, -3, -5, -6, -10, -15 and -30.
  3. Prime Factors of 30: 2, 3, 5.
  4. Prime Factorization of 30: 2 × 3 × 5 = 2 × 3 × 5.
  5. Sum of Factors of 30: 72.
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Which is the factor of 30?

The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. The factors of 31 are 1 and 31.

How do you prove root P is irrational?

Thus p is a common factor of a and b. But this is a contradiction, since a and b have no common factor. This contradiction arises by assuming √p a rational number. Hence,√p is irrational.

Can you divide a prime number by a prime number?

A prime number is an integer, or whole number, that has only two factors — 1 and itself. Put another way, a prime number can be divided evenly only by 1 and by itself. Prime numbers also must be greater than 1. For example, 3 is a prime number, because 3 cannot be divided evenly by any number except for 1 and 3.

What happens when you divide two prime numbers?

A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1. The only even prime number is 2. All other even numbers can be divided by 2.

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How do you prove that something is divisible by 24?

The reason for using 3 and 8 is that the least common multiple is 24. So every number that is divisible by both 3 and 8 is divisible by 24. It is not true that if a number’s divided by 6,4 then it is divided by 6⋅4 , as 12 proves. Yet it is true that if a number’s divided by 3,8 then it i divided by 3⋅8=24.

What is the remainder when p is divided by 30?

Show that if a prime number p is divided by 30, then the remainder is either a prime or 1. I did the sum sum but cannot complete it. I took p = 6 k + 1 and p = 6 k − 1 form. now for any k = 5 m we get 6 k = 30 m form so we can say that the remainder comes 1 but then I can’t give proper proof of the rest.

What is the remainder of the prime factors of 30?

The prime factors of 30 are 2, 3, and 5, and since p is prime, the remainder must contain the product of two primes both greater than 5, but then the remainder is greater than 30, a contradiction. You can contradict the statement by taking a number in the form of 30 q + n where n is any composite number between 1 and 30.

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What is a prime number?

A prime number is any integer, or whole number, greater than 1 that is only divisible by 1 and itself. In other words, a prime number only has two factors, 1 and itself. Is 2 a prime number? Yes, 2 is a prime number because it only has two factors, 1 and 2. Is 17 a prime number? Yes, 17 is a prime number because it only has two factors, 1 and 17.

What is a prime number with exactly two divisors?

A prime number is a positive integer with exactly two positive divisors. If p is a prime then its only two divisors are necessarily 1 and p itself, since every number is divisible by 1 and itself. The rst ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. It should be noted that 1 is NOT PRIME. Lemma.