Back to Ganita Prakash: Class 7 Mathematics, Par...BackConcept

What Happens When Numbers Are Doubled

Double both numbers and the HCF doubles. Find out when the HCF of two multiples of the same number is exactly that number.

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What Doubling Does

Doubling both numbers adds one 2 to each, so the HCF doubles.

Try it first (Math Talk, Textbook p. 59)

HCF of 6 and 9 is 3. Double both: 12 and 18. Their HCF is 6. It doubled.

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Doubling 270 and 50

The book's example of the HCF doubling.

Problem. Find the HCF of 270 and 50, then of 540 and 100. Then find the HCF of $14 \times 6$ and $14 \times 9$ . (Textbook p. 60)

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HCF of Multiples Card

What happens to the HCF when numbers are scaled.

Scaling and the HCF

Double both numbers and the HCF doubles: 270 and 50 → 10; 540 and 100 → 20.

HCF of k × a and k × b is at least k. It is exactly k when a and b have no common factor (co-prime).

Example:

14 \times 6

and

14 \times 9

. 6 and 9 share 3, so the HCF is

14 \times 3 = 42

Multiples of the Same Number

HCF of pairs built on the same multiplier.

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HCF of $18 \times 10$ and $18 \times 15$ ?

When Is the HCF the Multiplier?

Explore when the HCF equals the common multiplier.

When is the HCF the same as the common multiplier?

Textbook p. 60. In the four pairs above — $18 \times 10$ , $18 \times 15$ ; $10 \times 38$ , $10 \times 21$ ; $5 \times 13$ , $5 \times 20$ ; $12 \times 16$ , $12 \times 20$ — in which cases is the HCF the same as the common multiplier? Explore more examples and explain when this happens.

Which pairs?

List the letters.

When does it happen, and why?

Look at what is left after the common multiplier.

Two new examples of each kind

One where the HCF is the multiplier, one where it is bigger.

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