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Finding Common Ground

The biggest one they share

Ribbons of 12 m and 18 m. Cut equal pieces with nothing left over.

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Factors of 12: 1, 2, 3, 4, 6, 12.
Step 1 of 4
  1. Factors of 12: 1, 2, 3, 4, 6, 12.
  2. Factors of 18: 1, 2, 3, 6, 9, 18.
  3. Shared: 1, 2, 3, 6.
  4. Biggest shared factor: 6. HCF = 6.

The shared list has a top

A piece length must go into both 12 and 18. The longest such length is 6 m.

Both 12 and 18 share the factors 1, 2, 3 and 6. The biggest one is the highest common factor, or HCF.

HCF(12, 18) = 6 means: the HCF of 12 and 18 is 6.

Any two whole numbers share the factor 1. That is because 1 goes into every number. So HCF(8, 15) = 1.

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This track

  1. 0 Start here
  2. 1 The primes inside a number
  3. 2 A factor tree, and where it ends
  4. 3 The biggest one they share
  5. 4 Reading it off the two prime lists
  6. 5 When two step counts meet
  7. 6 The same two lists, read the other way
  8. 7 Which one does the question want?
  9. 8 Check it before you hand it in
  10. 9 Co-prime numbers
  11. 10 One table for the HCF and the LCM
  12. 11 The HCF, the LCM and the product
  13. 12 Checkpoint
  14. 13 The big picture
  15. 14 Track quiz

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