Finding Common Ground - Flash Cards
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What is the Highest Common Factor (HCF)?
The HCF is the largest number that is a factor of two or more numbers. It is also known as the Greatest Common Divisor (GCD).
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How do you find the HCF of two numbers?
To find the HCF, list all factors of both numbers and identify the largest common factor.
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Find the factors of 12.
The factors of 12 are 1, 2, 3, 4, 6, and 12.
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Find the factors of 16.
The factors of 16 are 1, 2, 4, 8, and 16.
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What are the common factors of 12 and 16?
The common factors are 1, 2, and 4.
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What size tiles should Sameeksha buy for a 12 ft by 16 ft room?
Sameeksha should buy 4 ft square tiles, using the largest common factor of the room dimensions.
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Find the HCF of 84 and 108.
The HCF of 84 and 108 is 12, which is the largest common factor.
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How do you determine the Least Common Multiple (LCM)?
The LCM is the smallest number that is a multiple of two or more numbers.
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What is an example of finding LCM using prime factorisation?
For numbers 14 (2 x 7) and 35 (5 x 7), the LCM is 70 (2 x 5 x 7).
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Explain prime factorisation.
Prime factorisation is expressing a number as a product of its prime factors.
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What is a prime number?
A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
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List the first five prime numbers.
The first five prime numbers are 2, 3, 5, 7, and 11.
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What is a conjecture in mathematics?
A conjecture is a statement that is believed to be true but has not been proven.
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How are HCF and LCM related?
The HCF and LCM of two numbers can be used to find one from the other using the formula: HCF × LCM = Product of the two numbers.
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What technique can be used for finding HCF quickly?
Prime factorisation can be used to quickly identify the HCF by taking the lowest powers of common prime factors.
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Provide an example of a common mistake when finding HCF.
A common mistake is forgetting to list all factors correctly, leading to identifying the wrong HCF.
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What is a factor?
A factor is a whole number that can be divided evenly into another number.
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What are multiples?
Multiples are the result of multiplying a number by an integer.
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How do you find common multiples of two numbers?
List the multiples of each number until you find the smallest common number.
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What is the prime factorization of 90?
The prime factorization of 90 is 2 × 3 × 3 × 5.
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What is the significance of the largest common factor?
The largest common factor helps in simplifying fractions and solving problems involving division of wholes.
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