Lesson Two: Prime Factors Math Worksheet With Answers printable pdf download

Lesson Two: Prime Factors Math Worksheet With Answers

Lesson Two: Prime Factors

Primes

Prime numbers �� are special integers whose only positive divisors are and ��. Thus,

we can see that 2, 3, 5, 7, 11, 13, … are all primes. Note that is the only even prime

number.

Primes are used to factor numbers; for example, 12 = 2

∗ 3. As you will see, prime

factorization provides a lot of useful information.

Problems

1) What is the largest two-digit prime number whose digits are also each prime?

First, note that the prime numbers that are also digits must be 2, 3, 5, of 7. Thus, the

largest tens digit possible is 7. Then, 77 and 75 are not prime, so our answer must

be 73.

2) What is the prime factorization of 2012?

Note that this is divisible by 4, which gives 503. To see if 503 is prime, we note that

we only have to check if it is divisible by the primes less then √ 503 ≈ 22 (why?), or

3, 5, 7, 11, 13, 17, 19. 503 is indeed prime, so our factorization is 2

∗ 503.

3) Find gcd(42,700) and lcm[6,8,14], where gcd is the greatest common divisor and

lcm is the least common multiple.

Prime factorization will help greatly here. We can see that 42 = 2 ∗ 3 ∗ 7 and

700 = 2

∗ 5

∗ 7. Thus, the gcd can only contain factors of 2 and 7 since they are the

only common factors. Our answer is 2 ∗ 7 = 14. Now, 6 = 2 ∗ 3, 8 = 2

, and

14 = 2 ∗ 7. With the lcm, we must take the maximum exponent of each prime factor

that exists: 2

∗ 3 ∗ 7.

In general, if �� and �� are two integers with prime factorizations

�� = ��

∗ ��

∗ … ∗ ��

��

�� = ��

∗ ��

∗ … ∗ ��

��

Lesson Two: Prime Factors Math Worksheet With Answers