Factors of 1212

Factors of 1212 are numbers that, when multiplied in pairs give the product as 1212. It has total 12 factors of which 1212 is the biggest factor and the prime factors of 1212 are 2, 3, 101. The sum of all factors of 1212 is 2856.

All Factors of 1212: 1, 2, 3, 4, 6, 12, 101, 202, 303, 404, 606 and 1212
Prime Factors of 1212: 2, 3, 101
Prime Factorization of 1212: 2² × 3¹ × 101¹
Sum of Factors of 1212: 2856

1.	What Are the Factors of 1212?
2.	Factors of 1212 by Prime Factorization
3.	Factors of 1212 in Pairs
4.	FAQs on Factors of 1212

What are Factors of 1212?

Factors of 1212 are pairs of those numbers whose products result in 1212. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1212?

To find the factors of 1212, we will have to find the list of numbers that would divide 1212 without leaving any remainder.

1212/101 = 12; therefore, 101 is a factor of 1212 and 12 is also a factor of 1212.
1212/6 = 202; therefore, 6 is a factor of 1212 and 202 is also a factor of 1212.

Similarly we can find other factors. Hence, the factors of 1212 are 1, 2, 3, 4, 6, 12, 101, 202, 303, 404, 606, 1212.

☛ Also Check:

Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, 75
Factors of 30 - The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
Factors of 5 - The factors of 5 are 1, 5
Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45
Factors of 56 - The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56

Factors of 1212 by Prime Factorization

The number 1212 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1212. The first step is to divide the number 1212 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1212 ÷ 2 = 606
606 ÷ 2 = 303

Further dividing 303 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 303 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 1212 can be written as 2² × 3¹ × 101¹ where 2, 3, 101 are prime.

Factors of 1212 in Pairs

Pair factors of 1212 are the pairs of numbers that when multiplied give the product 1212. The factors of 1212 in pairs are:

1 × 1212 = (1, 1212)
2 × 606 = (2, 606)
3 × 404 = (3, 404)
4 × 303 = (4, 303)
6 × 202 = (6, 202)
12 × 101 = (12, 101)

Negative pair factors of 1212 are:

-1 × -1212 = (-1, -1212)
-2 × -606 = (-2, -606)
-3 × -404 = (-3, -404)
-4 × -303 = (-4, -303)
-6 × -202 = (-6, -202)
-12 × -101 = (-12, -101)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 1212 Solved Examples

Example 1: How many factors are there for 1212?

Solution:

The factors of 1212 are too many, therefore if we can find the prime factorization of 1212, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 1212 = 2² × 3¹ × 101¹
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 1212 and 27.

Solution:

The factors of 1212 are 1, 2, 3, 4, 6, 12, 101, 202, 303, 404, 606, 1212 and factors of 27 are 1, 3, 9, 27.

Therefore, the Least Common Multiple of 1212 and 27 is 10908 and Greatest Common Divisor (GCD) of 1212 and 27 is 3.
Example 3: Find if 1, 3, 4, 6, 303, 606 and 826 are factors of 1212.

Solution:

When we divide 1212 by 826 it leaves a remainder. Therefore, the number 826 is not a factor of 1212. All numbers except 826 are factors of 1212.
Example 4: Find the product of all the prime factors of 1212.

Solution:

Since, the prime factors of 1212 are 2, 3, 101. Therefore, the product of prime factors = 2 × 3 × 101 = 606.

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FAQs on Factors of 1212

What are the Factors of 1212?

The factors of 1212 are 1, 2, 3, 4, 6, 12, 101, 202, 303, 404, 606, 1212 and its negative factors are -1, -2, -3, -4, -6, -12, -101, -202, -303, -404, -606, -1212.

What is the Sum of Factors of 1212?

Sum of all factors of 1212 = (2^{2 + 1} - 1)/(2 - 1) × (3^{1 + 1} - 1)/(3 - 1) × (101^{1 + 1} - 1)/(101 - 1) = 2856

What are the Prime Factors of 1212?

The prime factors of 1212 are 2, 3, 101.

What is the Greatest Common Factor of 1212 and 185?

The factors of 1212 are 1, 2, 3, 4, 6, 12, 101, 202, 303, 404, 606, 1212 and the factors of 185 are 1, 5, 37, 185. 1212 and 185 have only one common factor which is 1. This implies that 1212 and 185 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1212 and 185 is 1.

How Many Factors of 1211 are also common to the Factors of 1212?

Since, the factors of 1212 are 1, 2, 3, 4, 6, 12, 101, 202, 303, 404, 606, 1212 and factors of 1211 are 1, 7, 173, 1211. Hence, 1212 and 1211 have only one common factor which is 1. Therefore, 1212 and 1211 are co-prime.

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