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Factors of 76

Before learning about the factors of 76, here's a fact for you. Did you know that 76 is one of the two 2-digit numbers whose square and higher powers give a number that ends with 76? 76 is an even composite number with several positive and negative factors. In this lesson, we will calculate the factors of 76, the prime factors of 76, and the factors of 76 in pairs along with solved examples for a better understanding.

Factors of 76: 1, 2, 4, 19, 38, and 76
Prime Factorization of 76: 76 = 2 x 2 x 19

1. What Are the Factors of 76?
2. How to Calculate the Factors of 76?
3. Factors of 76 by Prime Factorization
4. Factors of 76 in Pairs
5. FAQs on Factors of 76

What Are the Factors of 76?

Factors of the number 76 are the numbers that completely divide 76. It means that if the remainder is zero, then the number is the factor of 76. Let's first see the numbers that completely divide 76.

The positive numbers are 1, 2, 4, 19, 38, and 76 which divide 76 completely. The negative numbers are -1, -2, -4, -19, -38, and -76 which divide 76 completely.

How to Calculate the Factors of 76?

Factors of a number can be calculated by many methods. One of the methods is dividing the number by the smallest of the factors. Factors of the number 76 can be calculated as follows:

Step 1: Write the smallest two factors of 76 (except for 1). The smallest two factors of 76 are 2 and 4.

Step 2: Divide 76 by 2 and 4.
76 ÷ 2 = 38
76 ÷ 4  = 19

Hence, 2, 4, 19, and 38 are the factors of 76.

Step 3: Include 1 and the number itself in the list of factors. Thus, the factors of 76 are 1, 2, 4, 19, 38, and 76.

Important Notes

  • 76 is one of the two 2-digit numbers whose square and higher powers give a number that ends with 76.
    762 = 5776
    763 = 438976
    764 = 33362176

  • 1 and the number itself is the factor of any number.

  • The numbers that have more than 2 factors are called composite numbers.

  • 1 is not a prime number; 2 is the smallest prime number.

Explore factors using illustrations and interactive examples

Factors of 76 by Prime Factorization

Let us find the prime factorization of 76 by expressing it as the product of prime numbers.

factor tree for 76
 

Hence, the prime factorization of 76 is 2 × 2 × 19.

From the prime factorization of 76, it is clear that 2 and 19 are the factors of 76. In fact, 2 and 19 are the prime factors of 76. Also, we know that 1 is a factor of every number.

Thus, the factors of 76 by prime factorization are 2 and 19.

Factors of 76 in Pairs

The pair of factors of number n is the set of two numbers which when multiplied together gives the number n.

Positive factors of 76 are 1, 2, 4, 19, 38, and 76.

Pairs of positive factors of 76 are (1, 76), (2, 38), and (4, 19).

1 × 76 = 2 × 38 = 4 × 19 = 76

Factors of 76 in pairs
 

Negative factors of 76 are -1, -2, -4, -19, -38, and -76.

Pairs of negative factors of 76 are (-1, -76), (-2, -38), and (-4, -19).

-1 ×  -76 = -2 × -38 = -4 × -19 = 76

 

Solved Examples

  1. Example 1 Sam wants to empty two buckets full of water. The buckets have a capacity of 76 liters and 56 liters. He wants to empty the buckets with the help of a glass. What should be the capacity of the glass such that no water remains in both the buckets?

    Solution:

    The capacity of one bucket = 76 liters

    The capacity of the other bucket = 56 liters

    To find the capacity of glass we need to calculate the HCF of 76 and 56

    76 = 2 × 2 × 19
    56 = 2 × 2 × 2 × 7

    HCF of 76 and 56 = 2 × 2 = 4

    Hence, Sam should use a glass with capacity of 4 liters.

  2. Example 2 Find the largest number which can divide 76, 304, and 228.

    Solution

    To find the largest number which can divide 76, 304, and 228, we need to calculate the HCF of these numbers.

    76 = 2 × 2 × 19
    304 = 2 × 2 × 2 × 2 × 19
    228 = 2 × 2 × 3 × 19

    HCF of 76, 304, and 228 is 2 × 2 × 19.

    Hence, 76 is the largest number which can divide 76, 304, 228.

  3. Example 3 Julia wants to add a natural number to 8 so that it will become a factor of 76. What number should she add?

    Solution

    Let's assume that she adds y to 8. Thus, ( y + 8) is a factor of 76.

    Let's write down all the factors of 76 that are greater than 8. They are 19, 38, and 76.

    y + 8 = 19
    y + 8 = 38
    y + 8 = 76

    From the above, we can say that y can take the values of 11, 30, or  68.

    Thus, Julia can add 11, 30, or 68 to 8.

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FAQs on Factors of 76

1. What are the factors of 76?

The factors of 76 are 1, 2, 4, 19, 38, and 76.

2. How many positive factors do 76 have?

Positive factors of 76 are 1, 2, 4, 19, 38, and 76. Thus, it has 6 positive factors.

3. Is 76 a prime number or a composite number?

76 is a composite number.

4. Why is 76 a composite number?

76 is a composite number because it can be expressed as the product of the following prime numbers: 76 = 2 x 2 x 19.

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