What times something equals to 84? Like this: ___×__= 84.
4 * 21 = 2 * 2 * 3 * 7
Simplify: 6a(4a - 2) + 3a(a + 7)
To find two numbers that multiply together to equal 84, you can use a method called guess and check or factorization.
1. Guess and Check Method:
Start with a number and divide 84 by that number to see if it evenly divides. Then, check if the quotient is a whole number. If it is, the pair of numbers is your answer. If not, try another number until you find the pair that multiplies to 84.
For example:
Let's start with 1.
84 divided by 1 equals 84, which is a whole number.
So, 1 and 84 are a pair that multiplies to 84.
2. Factorization Method:
To find the factors of 84, we can break it down into its prime factors.
Prime factorization of 84: 2 × 2 × 3 × 7
Now, we can group these factors into pairs in different combinations to get two numbers that multiply to 84. Remember, each pair of factors has to include exactly one of each prime factor.
Possible pairs:
(1 × 84), (2 × 42), (3 × 28), (4 × 21), (6 × 14), (7 × 12)
So, the possible pairs of numbers that multiply to 84 are:
1 × 84 = 84
2 × 42 = 84
3 × 28 = 84
4 × 21 = 84
6 × 14 = 84
7 × 12 = 84
Therefore, the pairs of numbers that multiply to 84 are 1 and 84, 2 and 42, 3 and 28, 4 and 21, 6 and 14, 7 and 12.