Numbers
About 6 min · Mathematics · English
Time worked out from the lesson's 404 words at 150 words a minute, plus a minute for each question.
Numbers form the foundation of mathematics and are a core component of the AP TET Mathematics section. This topic tests your understanding of whole numbers, integers, place value systems, divisibility rules, and methods for finding HCF and LCM—concepts that primary school teachers must explain clearly to young learners.
Key ideas
- Natural numbers are counting numbers starting from 1 (1, 2, 3, ...). Whole numbers include zero along with natural numbers (0, 1, 2, 3, ...).
- Integers extend whole numbers to include negative numbers (..., -3, -2, -1, 0, 1, 2, 3, ...). Every whole number is an integer, but not every integer is a whole number.
- Place value assigns a value to a digit based on its position. In 5,847, the digit 5 has place value 5,000 (thousands place), while face value remains 5.
- Divisibility means one number divides another exactly without remainder. If a divides b exactly, we write a | b.
- Factors are numbers that divide a given number exactly. Multiples are products of a number with natural numbers.
Watch out for
- Confusing place value with face value → Place value depends on position (7 in 472 has place value 70), while face value is the digit itself (7). Always identify what the question asks.
- Applying divisibility rule for 4 to the entire number → Only the last two digits matter for divisibility by 4. For 3,128, check if 28 is divisible by 4 (yes, 28 ÷ 4 = 7), not the whole number.
- Taking highest powers for HCF instead of lowest → HCF uses common factors with lowest powers; LCM uses all factors with highest powers. Reverse this and you'll swap answers.
Quick reference
- Whole numbers = 0, 1, 2, 3, ... (include zero; no negatives)
- Integers = ..., -2, -1, 0, 1, 2, ... (include negatives)
- Divisibility by 6 = must pass both divisibility by 2 AND 3
- HCF: common primes, lowest powers; LCM: all primes, highest powers
- HCF(a, b) × LCM(a, b) = a × b
Check yourself: 3 questions
1. A number when divided by 12 leaves a remainder of 7. What will be the remainder when the same number is divided by 6?
2. The HCF of two numbers is 18 and their LCM is 360. If one of the numbers is 72, what is the other number?
3. What is the smallest number that should be added to 2957 so that the resulting number is divisible by 11?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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