HCF & LCM from Prime Factors (Year 11)
Free printable UK Year 11 (GCSE Foundation) maths worksheet: use prime factorisations to find the HCF and LCM of two numbers, the unique-factorisation method.
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Grade 10 · Math worksheet
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Math
HCF & LCM from Prime Factors
Use prime factorisations (written in index notation) to find the HCF (lowest shared power of each common prime) and LCM (highest power of every prime present) of each pair of numbers.
- 1.Write 15 and 100 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 15 and 100.
- 2.Write 325 and 100 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 325 and 100.
- 3.Write 325 and 26 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 325 and 26.
- 4.Write 10 and 65 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 10 and 65.
- 5.Write 104 and 10 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 104 and 10.
- 6.Write 351 and 33 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 351 and 33.
- 7.Write 28 and 91 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 28 and 91.
- 8.A = 5² × 11 and B = 7 × 11 (A = 275, B = 77). Using these prime factorisations, find the HCF and LCM of A and B.
- 9.A = 7 × 11 and B = 7 × 13 (A = 77, B = 91). Using these prime factorisations, find the HCF and LCM of A and B.
- 10.A = 5 × 11 and B = 3² × 5 (A = 55, B = 45). Using these prime factorisations, find the HCF and LCM of A and B.
- 11.A = 2 × 7 and B = 2 × 11 (A = 14, B = 22). Using these prime factorisations, find the HCF and LCM of A and B.
- 12.A = 3 × 7 and B = 7 × 11 (A = 21, B = 77). Using these prime factorisations, find the HCF and LCM of A and B.
- 13.A = 7 × 11 and B = 5 × 7 (A = 77, B = 35). Using these prime factorisations, find the HCF and LCM of A and B.
- 14.For 325 and 104, the HCF is 13 and the LCM is 2600. Verify that HCF x LCM = 325 x 104, and state whether this is true.
- 15.For 65 and 91, the HCF is 13 and the LCM is 455. Verify that HCF x LCM = 65 x 91, and state whether this is true.
- 16.For 325 and 91, the HCF is 13 and the LCM is 2275. Verify that HCF x LCM = 325 x 91, and state whether this is true.
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