Study Guides/Maths/Factors of 56
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What are the Factors of 56?

The factors of a number are the building blocks that can be multiplied together to produce that exact number. Finding factors is a crucial skill for simplifying fractions and algebra.

Question (Click to Flip)

What is the sum of all the factors of 56?

Answer

If you add them all together: 1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120.

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Key Facts

We know 56 is not divisible by 3 because of the divisibility rule: Add the digits (5 + 6 = 11). Since 11 is not in the 3 times table, 56 is not divisible by 3.

A fast way to check if a number is divisible by 4 is if you can cut it in half twice. (Half of 56 is 28. Half of 28 is 14. Yes, it works).

1. What are the Factors of 56?

The number 56 has exactly 8 positive factors. The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, and 56.

2. Finding the Factor Pairs

The easiest way to find factors is to find their pairs. What two whole numbers multiply together to make 56?

  • $1 \times 56 = 56$
  • $2 \times 28 = 56$
  • $4 \times 14 = 56$
  • $7 \times 8 = 56$ Once the numbers in the pair get extremely close to each other (like 7 and 8), you know you have found all the possible pairs.

3. Prime Factorization of 56

If we want to break 56 down into only Prime Numbers (numbers that cannot be divided further):

  • Start by dividing by 2: $56 \div 2 = 28$
  • Divide by 2 again: $28 \div 2 = 14$
  • Divide by 2 again: $14 \div 2 = 7$
  • 7 is a prime number, so we stop here. The prime factorization of 56 is: $2 \times 2 \times 2 \times 7$ (or $2^3 \times 7$).

Questions and Answers

What is the sum of all the factors of 56?+

If you add them all together: 1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120.

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