What is the least perfect square that is a factor of 4536?
Answers
Answer:
there is no least perfect square that is factor of 4536.
Step-by-step explanation:
Step 1:
What is the last number of 4,536? It is this number: 4536. The answer is 6. Is 6 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?
Answer: NO, 6 is not in the list of numbers that are never perfect squares. Let's continue to the next step.
Step 2:
We now need to obtain the digital root of the number. Here's how you do it:
Split the number up and add each digit together:
4 + 5 + 3 + 6 = 18
If the answer is more than one digit, you would add each digit of the answer together again:
1 + 8 = 9
What is the digital root of number 4,536?
Answer: 9
Step 3:
So now we know the digital root of 4,536 is 9. Is 9 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
Answer: YES, 9 is in the list of digital roots that are always perfect squares. We can conclude that 4,536 could be a perfect square!
Factoring
OK, so now we know that 4,536 could be a perfect square. We have to find the factors of the number to be sure.
Here are all of the factors of 4,536:
1 x 4,5362 x 2,2683 x 1,5124 x 1,1346 x 7567 x 6488 x 5679 x 50412 x 37814 x 32418 x 25221 x 21624 x 18927 x 16828 x 16236 x 12642 x 10854 x 8456 x 8163 x 72
We're looking for a factor combination with equal numbers for X and Y (like 3x3) above. Notice there isn't a equal factor combination, that when multiplied together, produce the number 4,536. That means 4,536 is NOT a perfect square.
Given : Number 4536
To Find : least perfect square that is a factor of 4536
Solution:
All natural numbers have 1 as factor
4536 also has 1 as one of the factor.
1 is the lest perfect square .
Hence answer is 1
If Question is largest perfect square that is a factor of 4536
4536
2 2268
2 1134
2 567
3 189
3 63
3 21
3 7
7 1
4536 = 2 * 2 * 2 * 3 * 3 * 3 * 3 * 7
= 2² * 2 * 3² * 3² * 7
= (2 * 3 * 3)² * 2 * 7
= 18² * 14
largest perfect square is 18² = 324
324 is largest perfect square which is a factor of 4536
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