Factors of 390

The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, and 390.

Positive Factors: These are the positive numbers that divide 390 evenly. Positive factors: 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390

Negative Factors: These are the negative counterparts of the positive factors. Negative factors: -1, -2, -3, -5, -6, -10, -13, -15, -26, -30, -39, -65, -78, -130, -195, -390

Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 390 as the product. Prime factors: 2, 3, 5, 13

Prime Factorization: Prime factorization involves breaking 390 into its prime factors. It is expressed as: 390=2×3×5×13
 

There are various methods to find the factors of 390:

Methods to Find the Factors of 390:

1. Multiplication Method
2. Division Method
3. Prime Factor and Prime Factorization
4. Factor Tree

This breakdown helps in understanding the various factors of 390, whether they are positive or negative, and how prime factorization works for this number.
 

The multiplication method identifies pairs of numbers whose product is 390.

Step 1: Find pairs of numbers whose product equals 390.

Step 2: The factors are those numbers that, when multiplied, give 390.

Step 3: List the pairs of numbers whose product equals 390. A list of pairs whose product is 390 is given below:

• 1 × 390 = 390
• 2 × 195 = 390
• 3 × 130 = 390
• 5 × 78 = 390
• 6 × 65 = 390
• 10 × 39 = 390
• 13 × 30 = 390
• 15 × 26 = 390

Thus, the factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, and 390.
 

The division method finds the numbers that fully divide the given number. The steps are outlined below:

Step 1: Since every number is divisible by 1, 1 will always be a factor.

Example: 390÷1=390390 \div 1 = 390390÷1=390

Step 2: Move to the next integer. The factors of 390 include the number used to divide and the quotient obtained.

Thus, the factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, and 390.
 

Prime factors of 390 are obtained by dividing the number by its prime numbers. A number simplified using its prime factors and expressed in the form of prime factorization is the prime factorization of that number.

Prime Factors of 390: 2, 3, 5, 13 Prime Factorization of 390:

Divide 390 by 2: 390÷2=195

Divide 195 by 3: 195÷3=65

Divide 65 by 5: 65÷5=13

Divide 13 by 13: 13÷13=1

Prime factorization of 390: 2×3×5×13

The prime factorization of 390 can be visually represented using a factor tree. This helps in understanding how the number is broken down into its prime factors.

Factors of 390 in Pairs

Factors of 390 can be written in both positive and negative pairs. Their product will be equal to 390.

Positive Factor Pairs: (1, 390), (2, 195), (3, 130), (5, 78), (6, 65), (10, 39), (13, 30), (15, 26)

Negative Factor Pairs: (-1, -390), (-2, -195), (-3, -130), (-5, -78), (-6, -65), (-10, -39), (-13, -30), (-15, -26)
 

• Co-prime: Numbers having 1 as the only common factor. For example, 15 and 26 are co-prime because their greatest common factor (GCF) is 1.

• Perfect Square: The number we get when the same number is multiplied twice. For example, 1 is a perfect square because it is 1×1

• Prime Factors: Prime numbers that, when multiplied together, give a specific number as the product. For 390, the prime factors are 2, 3, 5, and 13.

• Factor Tree: A tree diagram used to represent the prime factors of a given number. It helps visualize how a number is broken down into its prime factors.

• Multiple: Numbers we get when another number multiplies the given number. For example, 78 is a multiple of 13 because 13×6=78