i can't figure out this problem.
the GCF of two numbers is 479. one number is even and the other number is odd. neither number is divisible by the other. what is the smallest that these two numbers could be?
OMG THANK YOU I HAD THIS 6TH GRADE 3-4 AND WAS SO CONFUSED
Well, the smallest even is 479x2
The smallest odd is 479x3
check my thinking.
958 and 1437
I had this promblem 2 Course 1 marthmatics common core ?
omggg. thanks so much I had this same exact problem course 1 lesson 4-4
Well, seems like those numbers are playing hard to get! Let's release the mathematical clowns to tackle this problem. Since the greatest common factor (GCF) is 479, it means that these two numbers have no common factors other than 1 and 479. Now, let's add some magic: let's say the odd number is 479 itself, and the even number is simply 2. Ta-da! The smallest they could be is 479 and 2. Voilà! Did that solve the problem or did I just add a little too much clown magic? 🤡
To find the smallest two numbers that satisfy the given conditions, we need to consider the properties of the greatest common factor (GCF).
The GCF is the largest integer that divides both numbers without leaving a remainder. In this problem, the GCF is 479.
Since the GCF is an odd number, both numbers cannot be odd, as an odd number is not divisible by another odd number. Therefore, one of the numbers must be even.
To find the smallest two numbers, we can start with the following steps:
1. Let one of the numbers be 2 (the smallest even number).
2. Divide the GCF (479) by 2: 479 ÷ 2 = 239.5. Since the GCF must be an integer, we can conclude that 2 cannot be the even number.
3. Increment the even number by 2 and repeat the previous step until we find a number that satisfies the conditions.
Let's try this method:
1. Let's assume the even number is 2.
2. Divide the GCF (479) by 2: 479 ÷ 2 = 239.5. Since it's not an integer, 2 is not the even number.
3. Try the next even number, 4.
4. Divide the GCF (479) by 4: 479 ÷ 4 = 119.75. Still not an integer, so 4 is not the even number.
5. Continue this process:
- 6 is not divisible (479 ÷ 6 = 79.8333...)
- 8 is not divisible (479 ÷ 8 = 59.875)
- 10 is not divisible (479 ÷ 10 = 47.9)
- 12 is not divisible (479 ÷ 12 = 39.9166...)
- 14 is not divisible (479 ÷ 14 = 34.2142...)
- 16 is divisible! (479 ÷ 16 = 29.9375)
Therefore, the smallest even number that satisfies the conditions is 16. Now let's find the odd number.
To find the odd number, simply divide the GCF by the even number we found:
479 ÷ 16 = 29.9375
The result is not an integer, so let's round it down to the nearest integer (because both numbers must be integers):
29 × 16 = 464
Therefore, the smallest two numbers that satisfy these conditions are 16 and 464.