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3 (a) Write 504 as the product of its prime factors - OCR - GCSE Maths - Question 3 - 2017 - Paper 1
Question 3
3 (a) Write 504 as the product of its prime factors. (b) Find the lowest common multiple (LCM) of 180 and 504.
Worked Solution & Example Answer:3 (a) Write 504 as the product of its prime factors - OCR - GCSE Maths - Question 3 - 2017 - Paper 1
Step 1
Write 504 as the product of its prime factors.
Answer
To express 504 as a product of its prime factors, we start by dividing it by the smallest prime numbers:
- Divide 504 by 2:
- Divide 252 by 2:
- Divide 126 by 2:
- Divide 63 by 3:
- Divide 21 by 3:
- 7 is a prime number.
Thus, the prime factorization of 504 is:
Step 2
Find the lowest common multiple (LCM) of 180 and 504.
Answer
To find the LCM of 180 and 504, we first find the prime factorizations of both numbers:
For 180:
- Divide 180 by 2:
- Divide 90 by 2:
- Divide 45 by 3:
- Divide 15 by 3:
- 5 is a prime number.
Thus, the prime factorization of 180 is:
Now, using the factorizations:
- 504:
- 180:
The LCM is found by taking the highest powers of each prime:
- For 2: max(3, 2) = 3
- For 3: max(2, 2) = 2
- For 5: max(0, 1) = 1
- For 7: max(1, 0) = 1
Thus: Calculating this gives: