I got this question`and I need help. The product of a 3 digit number and a 1 digit number is 3714. What is the 3 digit number?
well, just a few observations: either the one digit number is even, or both are even. (ends in a even digit, 4)
so the one digit number is 2,4,6,8
but dividing by 2 yields a four digit number..
dividing by 6, 619 and there you go.
the one digit number is ≥4
... 6 looks good for the one digit
To find the 3-digit number, let's begin by listing the factors or combinations of factors of 3714:
1 × 3714
2 × 1857
3 × 1238
6 × 619
Since we are looking for a 3-digit number, we can eliminate the second combination (2 × 1857) because it results in a 4-digit number. Now, let's check if any of the remaining combinations result in a 3-digit number:
1 × 3714 = 3714 (not a 3-digit number)
3 × 1238 = 3714 (not a 3-digit number)
6 × 619 = 3714 (not a 3-digit number)
None of the combinations give us a 3-digit number. Therefore, it is not possible to find a 3-digit number that, when multiplied by a 1-digit number, equals 3714.
To find the answer to this question, we need to determine the 3-digit number that, when multiplied by a 1-digit number, results in a product of 3714.
Let's break this down step by step:
Step 1: Prime factorize the number 3714
To prime factorize a number, we break it down into its prime factors (numbers that are only divisible by 1 and itself). In this case, we can find the prime factors of 3714 by dividing it by prime numbers starting from 2 and going up.
3714 ÷ 2 = 1857
1857 ÷ 3 = 619
619 ÷ 619 = 1
The prime factorization of 3714 is 2 × 3 × 619.
Step 2: Identify the 1-digit number
Since the prime factorization of 3714 contains only one 1-digit number (which is 2), we know that the 1-digit number is 2.
Step 3: Find the 3-digit number
To find the 3-digit number, we need to divide the original number (3714) by the value of the 1-digit number (which is 2).
3714 ÷ 2 = 1857
Therefore, the 3-digit number is 1857.
So, the 3-digit number is 1857.