Schooling · Class 7 · Mathematics · Finding Common Ground · Chapter on a page
CBSE Class 7 · Mathematics · NCERT Ganita Prakash-II
Finding Common Ground: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A factor of a number divides it…
- A multiple of a number is what you…
- Common factors are factors that two…
- The Highest Common Factor (HCF) is…
- Common multiples are multiples that…
- The Lowest Common Multiple (LCM) is…
- Every pair of numbers has 1 as a…
- Formulas and facts
- HCF of two numbers ≤ the smaller…
- LCM of two numbers ≥ the larger number
- HCF × LCM = a × b
- 1 is a common factor of every pair…
- If one number is a factor of…
- If one number is a multiple of…
- Watch out for
- Mixing up HCF and LCM
- Forgetting that 1 is always a common…
- Stopping the multiples list too…
- Thinking LCM can be smaller than…
- Confusing factors with multiples
What this chapter is about
This chapter teaches you how to find numbers that are shared by two or more numbers. When you look for a common ground between numbers, you search for values that connect them. The main ideas here are common factors and common multiples.
Key ideas
- A factor of a number divides it exactly with no remainder. For example, 4 is a factor of 12 because 12 ÷ 4 = 3 exactly.
- A multiple of a number is what you get when you multiply it by 1, 2, 3, and so on. For example, multiples of 5 are 5, 10, 15, 20, …
- Common factors are factors that two or more numbers share. The common factors of 12 and 18 are 1, 2, 3 and 6.
- The Highest Common Factor (HCF) is the largest of all common factors. HCF of 12 and 18 is 6.
- Common multiples are multiples that two or more numbers share. Common multiples of 4 and 6 include 12, 24, 36, …
- The Lowest Common Multiple (LCM) is the smallest common multiple (other than zero). LCM of 4 and 6 is 12.
- Every pair of numbers has 1 as a common factor. If the only common factor is 1, the numbers are called co-prime. For example, 8 and 15 are co-prime.
- LCM is always equal to or greater than the larger number. HCF is always equal to or smaller than the smaller number.
Formulas and facts to remember
- HCF of two numbers ≤ the smaller number.
- LCM of two numbers ≥ the larger number.
- For any two numbers a and b: HCF × LCM = a × b.
- 1 is a common factor of every pair of numbers.
- If one number is a factor of another, then that number itself is the HCF.
- If one number is a multiple of another, then that number itself is the LCM.
Common mistakes
- Mixing up HCF and LCM → Remember: HCF is the Highest common Factor (a divider), LCM is the Lowest common Multiple (a product pattern).
- Forgetting that 1 is always a common factor → Include 1 when you list common factors.
- Stopping the multiples list too early and missing the smallest common one → Keep listing until you find a match.
- Thinking LCM can be smaller than both numbers → LCM is always at least as large as the bigger number.
- Confusing factors with multiples → A factor divides the number; a multiple is the number multiplied.
Quick revision
- Factors divide a number exactly; multiples are products of a number with 1, 2, 3, …
- HCF is the greatest number that divides two or more numbers.
- LCM is the smallest number that is a multiple of two or more numbers.
- HCF × LCM = product of the two numbers.
- Numbers with only 1 as their common factor are co-prime.