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What is the prime factorisation method to find HCF of 441 and 630 and 945?
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What is the prime factorisation method to find HCF of 441 and 630 and ...
Prime Factorisation Method to Find HCF of 441, 630, and 945
Prime factorisation is a method used to find the Highest Common Factor (HCF) of two or more numbers. It involves finding the prime factors of each number and then determining the common factors.
To find the HCF of 441, 630, and 945 using the prime factorisation method, follow these steps:
Step 1: Find the Prime Factors of Each Number
1.1 Find the prime factors of 441:
To find the prime factors of 441, we start by dividing it by the smallest prime number, which is 2. Since 441 is not divisible by 2, we move on to the next prime number, which is 3. 441 divided by 3 is 147. Next, we divide 147 by 3 again, resulting in 49. Finally, 49 divided by 7 is 7. Since 7 is a prime number, we stop here. Therefore, the prime factors of 441 are 3, 3, 7, and 7, written as 3^2 x 7^2.
1.2 Find the prime factors of 630:
To find the prime factors of 630, we repeat the same process. 630 divided by 2 is 315. Next, we divide 315 by 3, resulting in 105. Then, 105 divided by 3 is 35. Finally, 35 divided by 5 is 7. Since 7 is a prime number, we stop here. Therefore, the prime factors of 630 are 2, 3, 3, 5, and 7, written as 2 x 3^2 x 5 x 7.
1.3 Find the prime factors of 945:
To find the prime factors of 945, we repeat the same process. 945 divided by 3 is 315. Next, we divide 315 by 3 again, resulting in 105. Then, 105 divided by 3 is 35. Finally, 35 divided by 5 is 7. Since 7 is a prime number, we stop here. Therefore, the prime factors of 945 are 3 x 3 x 5 x 7.
Step 2: Determine the Common Factors
2.1 Compare the prime factors:
To find the HCF, we need to determine the common factors among the prime factorisations of the given numbers. By comparing the prime factors of 441, 630, and 945, we can identify the common factors: 3 and 7.
Step 3: Multiply the Common Factors
3.1 Multiply the common factors:
To find the HCF, multiply the common factors. In this case, the common factors are 3 and 7. Multiplying 3 and 7 gives us the HCF: 3 x 7 = 21.
Therefore, the HCF of 441, 630, and 945 is 21.
Prime factorisation is a method used to find the Highest Common Factor (HCF) of two or more numbers. It involves finding the prime factors of each number and then determining the common factors.
To find the HCF of 441, 630, and 945 using the prime factorisation method, follow these steps:
Step 1: Find the Prime Factors of Each Number
1.1 Find the prime factors of 441:
To find the prime factors of 441, we start by dividing it by the smallest prime number, which is 2. Since 441 is not divisible by 2, we move on to the next prime number, which is 3. 441 divided by 3 is 147. Next, we divide 147 by 3 again, resulting in 49. Finally, 49 divided by 7 is 7. Since 7 is a prime number, we stop here. Therefore, the prime factors of 441 are 3, 3, 7, and 7, written as 3^2 x 7^2.
1.2 Find the prime factors of 630:
To find the prime factors of 630, we repeat the same process. 630 divided by 2 is 315. Next, we divide 315 by 3, resulting in 105. Then, 105 divided by 3 is 35. Finally, 35 divided by 5 is 7. Since 7 is a prime number, we stop here. Therefore, the prime factors of 630 are 2, 3, 3, 5, and 7, written as 2 x 3^2 x 5 x 7.
1.3 Find the prime factors of 945:
To find the prime factors of 945, we repeat the same process. 945 divided by 3 is 315. Next, we divide 315 by 3 again, resulting in 105. Then, 105 divided by 3 is 35. Finally, 35 divided by 5 is 7. Since 7 is a prime number, we stop here. Therefore, the prime factors of 945 are 3 x 3 x 5 x 7.
Step 2: Determine the Common Factors
2.1 Compare the prime factors:
To find the HCF, we need to determine the common factors among the prime factorisations of the given numbers. By comparing the prime factors of 441, 630, and 945, we can identify the common factors: 3 and 7.
Step 3: Multiply the Common Factors
3.1 Multiply the common factors:
To find the HCF, multiply the common factors. In this case, the common factors are 3 and 7. Multiplying 3 and 7 gives us the HCF: 3 x 7 = 21.
Therefore, the HCF of 441, 630, and 945 is 21.
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What is the prime factorisation method to find HCF of 441 and 630 and ...
Do it by succesive division
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