what the prime factorization of each number using exponents?
229308
Prime factorization is the breaking down of a number into the prime numbers that multiply to the original number. For example, the prime factorization of 12 is 2 * 2 * 3. We can add exponents when we have the same prime number occurring more than once. So, the prime factorization of 12 can also be written as 22 * 3.
536965
['250 is a composite number.', 'Prime factorization: 250 = 2 x 5 x 5 x 5, which can be written 250 = 2 x (5^3)', 'The exponents in the prime factorization are 1 and 3. ... ', 'Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250.', 'Factor pairs: 250 = 1 x 250, 2 x 125, 5 x 50, or 10 x 25.']
1180020
['The prime factorization of 40 is: 2 x 2 x 2 x 5.', 'The prime factorization of 63 is: 3 x 3 x 7.', 'The prime factors and multiplicities 40 and 63 have in common are: 1.', '1 is the gcf of 40 and 63.', 'gcf(40,63) = 1.']
771845
Prime factorization shows you the only way a number can be factored. The process of prime factorization breaks down a composite number into the prime numbers that, when multiplied together, give you that composite number. Every number's prime factorization is unique.
870281
['The prime factorization of 19 is: 19.', 'The prime factorization of 48 is: 2 x 2 x 2 x 2 x 3.', 'The prime factors and multiplicities 19 and 48 have in common are: 1.', '1 is the gcf of 19 and 48.', 'gcf(19,48) = 1.']
124427
The prime factorization of 3 is: 3. The prime factorization of 6 is: 2 x 3. The prime factors and multiplicities 3 and 6 have in common are: 3. 3 is the gcf of 3 and 6.
499734
Answer and Explanation: The prime factorization of 11 is 1 × 11. The number 11 is a prime number, because its only factors are 1 and itself.
952671
So the prime factorization of 60 is 2 × 2 × 3 × 5, which can be written as 2 2 × 3 × 5. The actual prime factors of 60 are 2, 3, and 5.
1171869
The prime factorization of 4 is: 2 x 2. The prime factorization of 7 is: 7. The prime factors and multiplicities 4 and 7 have in common are: 1. 1 is the gcf of 4 and 7.
177627
['List the prime factors of each number.', "Circle every common prime factor — that is, every prime factor that's a factor of every number in the set.", 'Multiply all the circled numbers. The result is the GCF.']
790480
['The prime factorization of 18 is: 2 x 3 x 3.', 'The prime factorization of 49 is: 7 x 7.', 'The prime factors and multiplicities 18 and 49 have in common are: 1.', '1 is the gcf of 18 and 49.', 'gcf(18,49) = 1.']
1027192
The orange divisor(s) above are the prime factors of the number 2,010. If we put all of it together we have the factors 2 x 3 x 5 x 67 = 2,010. It can also be written in exponential form as 21 x 31 x 51 x 671.
354634
When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number. For example, the number 36 can be written as a product of primes as: 36 = 2² x 3². The expression 2² x 3² is said to be the prime factorization of 36.
1336580
The prime factors of a number are all the prime numbers that, when multiplied together, equal the original number. You can find the prime factorization of a number by using a factor tree and dividing the number into smaller parts.
1450559
24 is a composite number. The exponents in the prime factorization are 3 and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 x 2 = 8. Therefore 24 has exactly 8 factors.
58425
Prime Factorization. "Prime Factorization" is finding which prime numbers multiply together to make the original number.
196323
73 is a prime number. The exponent of prime number 73 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 73 has exactly 2 factors.