The number of prime factors of (3 x 5)12 (2 x 7)10 (10)25 is:
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The question is: The number of prime factors of (3×5)×12(2×7)×10×10×25
The result is: 63,00,000.
The last digit of 6300000 is 0, which means it is even. Therefore 6300000 is divisible by 2:
6300000 = 2×3150000
The last digit of 3150000 is 0, which means it is even. Therefore 3150000 is divisible by 2:
3150000 = 2×1575000:
6300000 = 2×2×1575000
The last digit of 1575000 is 0, which means it is even. Therefore 1575000 is divisible by 2:
1575000 = 2×787500:
6300000 = 2×2×2×787500
The last digit of 787500 is 0, which means it is even. Therefore 787500 is divisible by 2:
787500 = 2×393750:
6300000 = 2×2×2×2×393750
The last digit of 393750 is 0, which means it is even. Therefore 393750 is divisible by 2:
393750 = 2×196875:
6300000 = 2×2×2×2×2×196875
196875 is not divisible by 2 since 196875 is odd and 2 is even:
6300000 = 2×2×2×2×2×196875 (196875 is not divisible by 2)
The sum of the digits of 196875 is 1 + 9 + 6 + 8 + 7 + 5 = 36, which is divisible by 3. This means 196875 is divisible by 3:
196875 = 3×65625:
6300000 = 2×2×2×2×2×3×65625 (65625 is not divisible by 2 since 196875 is not)
The sum of the digits of 65625 is 6 + 5 + 6 + 2 + 5 = 24, which is divisible by 3. This means 65625 is divisible by 3:
65625 = 3×21875:
6300000 = 2×2×2×2×2×3×3×21875 (21875 is not divisible by 2 since 65625 is not)
The sum of the digits of 21875 is 2 + 1 + 8 + 7 + 5 = 23, which is not divisible by 3. This means 21875 is not divisible by 3:
6300000 = 2×2×2×2×2×3×3×21875 (21875 is not divisible by 2 or 3)
The last digit of 21875 is 5, which means 21875 is divisible by 5:
21875 = 5×4375:
6300000 = 2×2×2×2×2×3×3×5×4375 (4375 is not divisible by 2 or 3 since 21875 is not)
The last digit of 4375 is 5, which means 4375 is divisible by 5:
4375 = 5×875:
6300000 = 2×2×2×2×2×3×3×5×5×875 (875 is not divisible by 2 or 3 since 4375 is not)
The last digit of 875 is 5, which means 875 is divisible by 5:
875 = 5×175:
6300000 = 2×2×2×2×2×3×3×5×5×5×175 (175 is not divisible by 2 or 3 since 875 is not)
The last digit of 175 is 5, which means 175 is divisible by 5:
175 = 5×35:
6300000 = 2×2×2×2×2×3×3×5×5×5×5×35 (35 is not divisible by 2 or 3 since 175 is not)
The last digit of 35 is 5, which means 35 is divisible by 5:
35 = 5×7:
6300000 = 2×2×2×2×2×3×3×5×5×5×5×5×7 (7 is not divisible by 2 or 3 since 35 is not)
The last digit of 7 is not 5 or 0, which means 7 is not divisible by 5:
6300000 = 2×2×2×2×2×3×3×5×5×5×5×5×7 (7 is not divisible by 2, 3 or 5)
No primes less than 7 divide into it. Therefore 7 is prime:
6300000 = 2×2×2×2×2×3×3×5×5×5×5×5×7
There are 5 copies of 2, 2 copies of 3, 5 copies of 5 and 1 copy of 7 in the product:
Answer: 6300000 = 2^5×3^2×5^5×7
The result is: 63,00,000.
The last digit of 6300000 is 0, which means it is even. Therefore 6300000 is divisible by 2:
6300000 = 2×3150000
The last digit of 3150000 is 0, which means it is even. Therefore 3150000 is divisible by 2:
3150000 = 2×1575000:
6300000 = 2×2×1575000
The last digit of 1575000 is 0, which means it is even. Therefore 1575000 is divisible by 2:
1575000 = 2×787500:
6300000 = 2×2×2×787500
The last digit of 787500 is 0, which means it is even. Therefore 787500 is divisible by 2:
787500 = 2×393750:
6300000 = 2×2×2×2×393750
The last digit of 393750 is 0, which means it is even. Therefore 393750 is divisible by 2:
393750 = 2×196875:
6300000 = 2×2×2×2×2×196875
196875 is not divisible by 2 since 196875 is odd and 2 is even:
6300000 = 2×2×2×2×2×196875 (196875 is not divisible by 2)
The sum of the digits of 196875 is 1 + 9 + 6 + 8 + 7 + 5 = 36, which is divisible by 3. This means 196875 is divisible by 3:
196875 = 3×65625:
6300000 = 2×2×2×2×2×3×65625 (65625 is not divisible by 2 since 196875 is not)
The sum of the digits of 65625 is 6 + 5 + 6 + 2 + 5 = 24, which is divisible by 3. This means 65625 is divisible by 3:
65625 = 3×21875:
6300000 = 2×2×2×2×2×3×3×21875 (21875 is not divisible by 2 since 65625 is not)
The sum of the digits of 21875 is 2 + 1 + 8 + 7 + 5 = 23, which is not divisible by 3. This means 21875 is not divisible by 3:
6300000 = 2×2×2×2×2×3×3×21875 (21875 is not divisible by 2 or 3)
The last digit of 21875 is 5, which means 21875 is divisible by 5:
21875 = 5×4375:
6300000 = 2×2×2×2×2×3×3×5×4375 (4375 is not divisible by 2 or 3 since 21875 is not)
The last digit of 4375 is 5, which means 4375 is divisible by 5:
4375 = 5×875:
6300000 = 2×2×2×2×2×3×3×5×5×875 (875 is not divisible by 2 or 3 since 4375 is not)
The last digit of 875 is 5, which means 875 is divisible by 5:
875 = 5×175:
6300000 = 2×2×2×2×2×3×3×5×5×5×175 (175 is not divisible by 2 or 3 since 875 is not)
The last digit of 175 is 5, which means 175 is divisible by 5:
175 = 5×35:
6300000 = 2×2×2×2×2×3×3×5×5×5×5×35 (35 is not divisible by 2 or 3 since 175 is not)
The last digit of 35 is 5, which means 35 is divisible by 5:
35 = 5×7:
6300000 = 2×2×2×2×2×3×3×5×5×5×5×5×7 (7 is not divisible by 2 or 3 since 35 is not)
The last digit of 7 is not 5 or 0, which means 7 is not divisible by 5:
6300000 = 2×2×2×2×2×3×3×5×5×5×5×5×7 (7 is not divisible by 2, 3 or 5)
No primes less than 7 divide into it. Therefore 7 is prime:
6300000 = 2×2×2×2×2×3×3×5×5×5×5×5×7
There are 5 copies of 2, 2 copies of 3, 5 copies of 5 and 1 copy of 7 in the product:
Answer: 6300000 = 2^5×3^2×5^5×7
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(3^12) (5^12) (2^10) (7^10) (2x5)^25
(2^10.2^25) (3^12) (5^12.5^25) (7^10)
2^35. 3^12. 5^37. 7^10
(2^10.2^25) (3^12) (5^12.5^25) (7^10)
2^35. 3^12. 5^37. 7^10
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