Factors of 276
Factors of 276 are integers that can be divided evenly into 276. There are 12 factors of 276 of which 276 itself is the biggest factor and its prime factors are 2, 3, 23 The sum of all factors of 276 is 672.
- All Factors of 276: 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138 and 276
- Prime Factors of 276: 2, 3, 23
- Prime Factorization of 276: 22 × 31 × 231
- Sum of Factors of 276: 672
1. | What Are the Factors of 276? |
2. | Factors of 276 by Prime Factorization |
3. | Factors of 276 in Pairs |
4. | FAQs on Factors of 276 |
What are Factors of 276?
Factors of 276 are pairs of those numbers whose products result in 276. These factors are either prime numbers or composite numbers.
How to Find the Factors of 276?
To find the factors of 276, we will have to find the list of numbers that would divide 276 without leaving any remainder.
- 276/138 = 2; therefore, 138 is a factor of 276 and 2 is also a factor of 276.
- 276/12 = 23; therefore, 12 is a factor of 276 and 23 is also a factor of 276.
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- Factors of 14 - The factors of 14 are 1, 2, 7, 14
- Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63
Factors of 276 by Prime Factorization
- 276 ÷ 2 = 138
- 138 ÷ 2 = 69
Further dividing 69 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 69 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 276 can be written as 22 × 31 × 231 where 2, 3, 23 are prime.
Factors of 276 in Pairs
Pair factors of 276 are the pairs of numbers that when multiplied give the product 276. The factors of 276 in pairs are:
- 1 × 276 = (1, 276)
- 2 × 138 = (2, 138)
- 3 × 92 = (3, 92)
- 4 × 69 = (4, 69)
- 6 × 46 = (6, 46)
- 12 × 23 = (12, 23)
Negative pair factors of 276 are:
- -1 × -276 = (-1, -276)
- -2 × -138 = (-2, -138)
- -3 × -92 = (-3, -92)
- -4 × -69 = (-4, -69)
- -6 × -46 = (-6, -46)
- -12 × -23 = (-12, -23)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 276 Solved Examples
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Example 1: How many factors are there for 276?
Solution:
The factors of 276 are too many, therefore if we can find the prime factorization of 276, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is ax × by × cz 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 276 = 22 × 31 × 231
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12 -
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 276 and 84.
Solution:
The factors of 276 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276 and factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Therefore, the Lowest Common Multiple (LCM) of 276 and 84 is 1932 and Greatest Common Divisor (GCD) of 276 and 84 is 12. -
Example 3: Find if 2, 3, 23, 46, 69, 92 and 209 are factors of 276.
Solution:
When we divide 276 by 209 it leaves a remainder. Therefore, the number 209 is not a factor of 276. All numbers except 209 are factors of 276.
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Example 4: Find the product of all the prime factors of 276.
Solution:
Since, the prime factors of 276 are 2, 3, 23. Therefore, the product of prime factors = 2 × 3 × 23 = 138.
FAQs on Factors of 276
What are the Factors of 276?
The factors of 276 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276 and its negative factors are -1, -2, -3, -4, -6, -12, -23, -46, -69, -92, -138, -276.
What is the Sum of all the Factors of 276?
Sum of all factors of 276 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (231 + 1 - 1)/(23 - 1) = 672
What are Prime Factors of 276?
The prime factors of 276 are 2, 3, 23.
What is the Greatest Common Factor of 276 and 267?
The factors of 276 and 267 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276 and 1, 3, 89, 267 respectively.
Common factors of 276 and 267 are [1, 3].
Hence, the Greatest Common Factor of 276 and 267 is 3.
How Many Factors of 276 are also common to the Factors of 204?
Since, the factors of 276 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276 and the factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204.
Hence, [1, 2, 3, 4, 6, 12] are the common factors of 276 and 204.
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