What equals 81 in multiplication?
Understand the Problem
The question is asking for the pairs of numbers that can be multiplied together to result in 81. We will explore the factors of 81 to find these pairs.
Answer
(1, 81), (3, 27), (9, 9)
Answer for screen readers
The pairs of numbers that multiply to 81 are: (1, 81), (3, 27), and (9, 9)
Steps to Solve
["1. Identify factors of 81 by trial division\n\nWe start by finding the smallest factors of 81 by dividing it by integers starting from 1 upwards. Since 1 $\times$ 81 = 81, (1, 81) is a pair.\n\n","2. Continue with higher integer divisions\n\nDivide 81 by integers greater than 1 to find more pairs of factors:\n\n- 81 $\times$ 2 is not an integer division.\n\n- 81 $\times$ 3 = 27, so (3, 27) is a pair.\n\n- Continue to 4 through 8, none are integer divisions.\n\n- 9 $\times$ 9 = 81, so (9, 9) is a pair.\n\n- Continue with integers > 9 won't provide new pairs as we repeat previous ones because multiplication is commutative."]
The pairs of numbers that multiply to 81 are: (1, 81), (3, 27), and (9, 9)
More Information
The number 81 is equivalent to $3^4$ which means it can be factored using multiples of 3. Multiplication is commutative, hence pairs like (1, 81) and (81, 1) are same.
Tips
A common mistake is not considering all possible pairs or forgetting that multiplication is commutative, thus missing pairs like (3, 27) and (27, 3).
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