Video: Using Prime Factorization to Find the Factors of a Given Number

How many prime factors does 76 have without repetition?

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Video Transcript

How many prime factors does 76 have without repetition?

In order for us to calculate how many prime factors 76 has without repetition, we’ll first need to find all the prime factors of 76. We can do that with a factor tree. 76 is an even number, and that means we know it has a prime factor of two. We want to find out how many times 76 is divisible by two. And so we say two goes into seven three times with the remainder of one. Two goes into 16 eight times with the remainder of zero. Two times 38 equals 76. But 38 is not a prime number. In fact, 38 is an even number and is therefore divisible by two.

So we divide 38 by two. Two goes into three one time with the remainder of one. Two goes into 18 nine times. Two times 19 equals 38. At this point, we recognize something about 19. 19 is a prime number, which means we’ve completed our factor tree. Two is prime and 19 is prime. And so the prime factorization of 76 is two times two times 19. But our question is “how many prime factors does 76 have without repetition?” And that means we’ll only count the factor of two once. This means 76 has two unique prime factors.

76 has two prime factors without repetition.

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