6.24 can be expressed as the product of two numbers in 4 different ways: 24 x 1, 12 x 2,8 x3 and 4 x 6. In how many different ways can 42 be expressed as a product of two numbers? * O (A) 3 O (B) 4 O (C) 5 O (D) 6
Answers
Answer:
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Step-by-step explanation:
Answer:
Total Different ways = 4
That is,
1 × 42
2 × 21
3 × 14
6 × 7
Option B is correct
Step-by-step explanation:
Usually what we must do is try to factor out and do it in a trial and error way
But there will always be an easier method.
Now,
24 = 1 × 24
24 = 2 × 12
24 = 3 × 8
24 = 4 × 6
What can we tell about 1, 2, 3, 4, 6, 8, 12, and 24.
Yes they are actually the factors of 24.
Then,
24 has 8 total factors, and can be represented in 4 different ways. So a brilliant observation is that,
Total different ways = (Number of factors)/2
Now, we can simply do it for 42
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
(Also, this can be used as a converse also, now on finding factors will be easy for you, what we must do is divide 42 by 1, we get 42
So,
Factors = 1, 42
Leave a gap in between, again do it for 2, we get 21
So,
Factors = 1, 2, 21, 42
Incase you don't get a whole number it means both are not the factors
For ex. Let's try if 5 is a factor of 42
42 ÷ 5 = 8.4
Since 8.4 is not a whole number, 5 is not a factor and you can skip 5 and go for 6.
We can keep doing it till we get a closer number, for example in 42, we get 6 × 7 = 42, which means there are no more factors and you can stop.)
So,
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
No. of Factors = 8
So,
Total Different ways = 8/2
Total Different ways = 4
That is,
1 × 42
2 × 21
3 × 14
6 × 7
Hope it helped you and believing you understood it...All the best