As your math tutor, I’m here to help you break down factor pairs of 546 step by step!
Factor pairs of 546 are any two numbers that, when multiplied together, equal 546. The question to ask is “what two numbers multiplied together equal 546?” Every factor can be paired with another factor, and multiplying the two will result in 546.
To find the factor pairs of 546, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 546. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.
Step 2:
Divide 546 by the smallest prime factor, in this case, 2:
546 ÷ 2 = 273
2 and 273 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 273 as the new focus. Find the smallest prime factor that isn’t 1, and divide 273 by that number. In this case, 3 is the new smallest prime factor:
273 ÷ 3 = 91
Remember that this new factor pair is only for the factors of 273, not 546. So, to finish the factor pair for 546, you’d multiply 2 and 3 before pairing with 91:
2 x 3 = 6
Step 4:
Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.
Here are all the factor pairs for 546:
(1, 546), (2, 273), (3, 182), (6, 91), (7, 78), (13, 42), (14, 39), (21, 26)
So, to list all the factors of 546: 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The negative factors of 546 would be: -1, -2, -3, -6, -7, -13, -14, -21, -26, -39, -42, -78, -91, -182, -273, -546
Now you’ve got it! A math tutor would always encourage you to practice with different numbers to reinforce your understanding of factor pairs. Try another one!