What are the Factors of 76?
As we already know, the factors of 76 are natural numbers that can divide 76 without a remainder. In other words, these natural numbers which are multiplied with other numbers to result in 76 as the product are known as the factors of 76.
Factors of 76 are 1, 2, 4, 19, 38 and 76.
In the table we can observe the factors, factor pairs as well as the prime factorization of 76.
Deriving the Factor list of 76
With the assistance of the divisibility rules in addition to the division facts linked to natural numbers, we can derive the list of factors for 76.
Prime factorization of 76
If a natural number can be expressed as a product of prime numbers, these prime numbers are known as the prime factors of that natural number. The process of expressing a number as the product of its prime factors is known as prime factorization.
The prime factors of the number 76 can be calculated by the factor tree method.
From the image we can see that the prime factorization of 76 is, 76 = 2 x 2 x 19
So, the prime factorization of 76 is 2\(^2\) x 19, this means 2 and 19 are the prime factors of 76.
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Positive factor pairs of 76
The factor pairs of 76 are a set of two integers, when multiplied together results in 76 as the product.
Solved Factors of 76 Examples
Example 1: Find the common factors of 35 and 76.
Solution:
Factors of 35 are 1, 5, 7, and 35.
Factors of 76 are 1, 2, 4, 19, 38 and 76.
So the common factor of 35 and 76 is 1.
Example 2: Tom wants to empty two cans full of juice. The cans each have a capacity of 22 liters and 24 liters. He wants to empty the cans by using a bottle. What should be the capacity of the bottle he uses such that no juice is left in both the cans?
Solution:
The capacity of first can = 22 liters
The capacity of the second can = 24 liters
To find the capacity of the bottle we need to calculate the GCF of 22 and 24
22 = 2 × 11
24 = 2 × 2 × 3
Hence, the GCF of 22 and 24 is 2.
So, Tom should use a bottle with a capacity of 2 liters to empty the cans such that no juice is left.
Example 3: What natural number should be added to 24 so that it will become a factor of 76.
Solution:
Let y a natural number to be added to 24 so that it will divide 76 completely.
Factors of 76 are 1, 2, 4, 19,38 and 76.
y + 24 must be 38 or 76.
i) y + 24 = 38
y = 14
ii) y + 24 = 76
y = 52
So, number 14 or 52 can be added to 24 to become a factor of 24.
Yes, 1 is a factor of 76. When you divide 76 by 1 you will get a quotient as 76 and remainder as zero.
Positive factor of 76: 1, 2, 4, 19, 38, and 76. So, there are 6 positive factors of 76.
76 is a composite number because 76 can be expressed as a product of prime factors.
Negative factor pairs are the two negative numbers which multiplied together give the result as 76.
Negative factor pairs of 76 are (-1, -76), (-2, -38), and
(-4, -19)