Using repeated devison method find the prime factors of the following numbers. 1. 28
Answers
Answer:
First, let us consider 22.
We will find the factors of 22 with repeated division.
The lowers prime number is 2 and the number 22 is divisible by 22.
Therefore, 22 = 2 × 11
The number cannot be factorised further as 11 is a prime number.
Therefore, prime factors of 22 = 2 × 11 × 1
Next, we will factorise 63.
The lowest prime number that can divide 63 is 3.
Thus 63 = 3 × 21
On division, the quotient is 21, which is again divisible by 3.
So, 63 = 3 × 3 × 7
The quotient now is 7 and it is divisible by 7 itself, as 7 is a prime number.
Thus 63 = 3 × 3 × 7 × 1
Another way to represent continuous division is as follows:
3|63−−−3|21−−−7|7−− 1
Thus, prime factors of 63 = 3 × 3 × 7 × 1
Now, we will see one more example.
Let us factorise 120.
The lowest prime number that can divide 120 is 2.
Thus, 120 = 2 × 60
The quotient is 60. It can also be divided by 2.
120 = 2 × 2 × 30
The quotient now is 30. It is also completely divisible by 2.
120 = 2 × 2 × 2 × 15
15 cannot be divided by 2, so we move to the next prime number, that is 3. It can completely divide 15.
120 = 2 × 2 × 2 × 3 × 5
The quotient 5 cannot be divided by 3, but it is divisible by 5 which is next prime number.
Thus, 120 = 2 × 2 × 2 × 3 × 5 × 1
In compact representation:
2|120−−−−2|60−−−2|30−−−3|15−−−5|5−− 1
Hence, prime factors of 120 = 2 × 2 × 2 × 3 × 5 × 1
Now, we will solve for other numbers in compact form.
3. 35
5|35−−−7|7−− 1
Hence, prime factors of 35 = 5×7×1.
4. 44
2|44−−−2|22−−−11|11−−− 1
Prime factors of 44 = 2×2×11×1.
5. 49
7|49−−−7|7−− 1
Prime factors of 49 = 7×7×1.
6. 48
2|48−−−2|24−−−2|12−−−2|6−−3|3−− 1
Prime factors of 48 = 2×2×2×2×3×1
7. 50
2|50−−−5|25−−−5|5−− 1
Prime factors of 50 = 2×5×5×1
8. 65
5|65−−−13|13−−− 1
Prime factors of 65 = 5×13×1
9. 87
3|87−−−29|29−−− 1
Prime factors of 87 = 3×29×1
10. 120
2|120−−−−2|60−−−2|30−−−3|15−−−5|5−− 1
Prime factors of 12 = 2×2×3×5
Note: Any numbers can be factored in the similar manner, either using compact representation or textual representation. A number will always be divisible by any of its prime factors and also a combination of factors.
Step-by-step explanation: