Find Prime Factorization/Factors Of 8 - Cuemath

What are Factors of 8?

Factors of 8 are those numbers that completely divide it leaving 0 as the remainder. For example, 8 ÷ 1 leaves a remainder 0.

We get 8 as the quotient and 0 as the remainder. This indicates that 8 is divisible by 1. Similarly,

• 8 ÷ 2 = 4
• 8 ÷ 4 = 2
• 8 ÷ 8 = 1

Thus, the factors of 8 are 1, 2, 4, and 8.

How to Calculate the Factors of 8?

We can use different methods to find the factors of 8 such as the prime factorization method and the division method. In prime factorization, we express 8 as the product of its prime factors and in the division method, we look for numbers that divide 8 exactly without a remainder.

Factors of 8 By Division Method

We know that 8 is a composite number and it will have prime factors. Let us calculate the prime factors of the number 8. The first step is to divide 8 with the smallest prime factor, which is 2, followed by the others.

• 8 ÷ 2 = 4
• 8 ÷ 4 = 2
• 8 ÷ 8 = 1

The division here shows that the number 8 is exactly divisible by 1, 2, 4, and 8. Hence, the total factors of 8 by division method are 1, 2, 4, and 8.

Factors of 8 By Prime Factorization

The factors of 8 can be represented by the upside-down division method as:

Method 1;

The factors of 8 can be represented by the factor tree method as:

Method 2:

The factors of 8 by the prime factorization method are 1, 2, 4, and 8. Here, 2 is the prime factor of 8. Explore factors using illustrations and interactive examples:

• Factors of 9 - The factors of 9 are 1, 3, and 9.
• Factors of 10 - The factors of 10 are 1, 2, 5, and 10.
• Factors of 15 - The factors of 15 are 1, 3, 5, and 15.
• Factors of 180 - The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
• Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20

Think Tank:

• Can you think of all the possible pair factors of 8?
• Can multiples of 8 also be the factors of 8?

Factors of 8 in Pairs

To find the factors of 8 in pairs, multiply the two numbers in a pair to get the resultant number as 8.

• Since 1 × 8 = 8, (1, 8) is a pair factor of 8. Similarly,
• 2 × 4 = 8, thus, (2, 4) is a pair factor of 8.
• Therefore, (8, 1) and (2, 4) are the factors of 8 in pairs.
• Factors of 8 can be represented as negative pair factors as well. For example, -8 × -1 = 8, thus, (-8, -1) is a negative pair factor of 8.

Important Notes:

• The factors of 8 are 1, 2, 4, and 8.
• 1 is a universal factor because it is a factor of all numbers.
• Factors are quite often given as pairs of numbers which when multiplied together give the original number.
• The factors of 8 in pairs are (2, 4) and (1, 8).
• 2 is the prime factor of 8.

Factors of 8 Solved Examples

1. Example 1: Kevin was asked to find the factors of 8 and 18. What will be his answer?

   Solution:

   Factors of 8 are 1, 2, 4, and 8 and the factors of 18 are 1, 2, 3, 6, 9, and 18.

2. Example 2: The following numbers were given to Mike and he was asked to find the number that was not a factor of 8. Help Mike find that number.

   1, 2, 3, 4, 5, 6, 7, and 8.

   Solution:

   Factors of 8 are 1, 2, 4, and 8. When we divide 8 by 3, 5, 6, and 7, it leaves a reminder.

   Thus, these numbers are not the factors of 8 which means 3, 5, 6, and 7 are not the factors of 8.

3. Example 3: What are the negative pair factors of 8?

   Solution:

   To find the negative pair factors, we take the following steps:-2 × -4 = 8

   -8 × -1 = 8

   Therefore, the negative pair factors of 8 are (-2, -4) and (-8, -1).

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FAQs on Factors of 8

What are the Factors of 8?

The factors of 8 are 1, 2, 4, 8 and its negative factors are -1, -2, -4, -8.

How Many Factors of 8 are also common to the Factors of 4?

Since, the factors of 8 are 1, 2, 4, 8 and the factors of 4 are 1, 2, 4. Hence, [1, 2, 4] are the common factors of 8 and 4.

What is the Sum of the Factors of 8?

All the Factors of 8 are 1, 2, 4, 8 and therefore the sum of all these factors is 1 + 2 + 4 + 8 = 15

What is the Greatest Common Factor of 8 and 5?

The factors of 8 are 1, 2, 4, 8 and the factors of 5 are 1, 5. 8 and 5 have only one common factor which is 1. This implies that 8 and 5 are co-prime. Hence, the Greatest Common Factor (GCF) of 8 and 5 is 1.

What are the Pair Factors of 8?

The pair factors of 8 are (1, 8), (2, 4).