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Numerical Ability lesson

Number Sense: Divisibility, Primes, GCF and LCM

Test divisibility without dividing, list factors in pairs, spot primes, and find the GCF and LCM with prime factors. These are the building blocks for fractions and word problems.

30 min read · Professional and Sub-Professional

What it is

Number sense here means knowing how whole numbers are built from smaller numbers. You will learn to:

  • tell if a number can be divided exactly by 2, 3, 4, 5, 6, 8, 9 or 10 without doing the division;
  • list all the factors of a number and the first few multiples;
  • tell a prime number from a composite number;
  • break a number into primes (prime factorization);
  • find the GCF (greatest common factor) and the LCM (least common multiple).

Why it matters on the exam

The Numerical Ability part of the exam has computation items that ask directly for a GCF, an LCM, a prime or a divisor. Word problems hide them too: "the largest number of identical kits" is a GCF, and "when will the buses leave together again" is an LCM.

These skills also power the next lessons. You reduce fractions with the GCF and add fractions with the LCM (the least common denominator). Quick divisibility checks also help you eliminate wrong choices fast.

Rule 1 of 10Ending tests: 2, 5 and 10 (last digit); 4 and 8 (last two or three digits)
Look only at the end of the number. By 2: the ones digit is even (0, 2, 4, 6, 8). By 5: the ones digit is 0 or 5. By 10: the ones digit is 0. By 4: the last two digits form a number divisible by 4. By 8: the last three digits form a number divisible by 8.
Worked example 1 of 4Two tests at once: divisible by 4 and by 9
Which of the following numbers is divisible by both 4 and 9?
  1. 1,836
  2. 2,754
  3. 3,412
  4. 4,626
Step 1 · Pick the testsDivisible by 4 → check the last two digits. Divisible by 9 → check the digit sum. A number must pass both.
Read the full lesson

The rest of this lesson, and every other lesson, is part of ReviewTayo.

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In the full lesson

  • How to recognize it on the test
  • What to look for (5 checks)
  • All 10 rules and tools
  • 4 worked examples, every step explained
  • 6 common mistakes and how to fix them
  • 3 exam techniques
  • Remember: 5 key points
  • Practice questions with explanations, and your progress saved
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More Numerical Ability lessons

ReviewTayo has 51 lessons that follow the official scope of the exam, each with rules, worked examples, common mistakes and practice. Open one and read the first part.

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