3. Playing with Numbers Mathematics Exercise - 3.6 class 6 Maths in English - CBSE Study
NCERT Solutions for Class 6 Mathematics are carefully prepared according to the latest CBSE syllabus and NCERT textbooks to help students understand every concept clearly. These solutions cover all important 3. Playing with Numbers with detailed explanations and step-by-step answers for better exam preparation. Each Exercise 3.6 is explained in simple language so that students can easily grasp the fundamentals and improve their academic performance. The study material is designed to support daily homework, revision practice, and final exam preparation for Class 6 students. With accurate answers, concept clarity, and structured content, these NCERT solutions help learners build confidence and score higher marks in their examinations. Whether you are revising a specific topic or preparing an entire chapter, this resource provides reliable and syllabus-based guidance for complete success in Mathematics.
Class 6 English Medium Mathematics All Chapters:
3. Playing with Numbers
6. Exercise 3.6
Exercise -3.6
Q1. Find the H.C.F. of the following numbers:
(f) 34, 102
Solutions:
Prime factorization of 34
= 2 × 17
Prime factorization of 102
= 2 × 3 × 17
HCF of 34 and 102 is 2 × 17
= 34
(g) 70, 105, 175
Solution:
Prime factorization of 70
= 2 × 5 × 7
Prime factorization of 105
= 3 × 5 × 7
Prime factorization of 175
= 5 × 5 × 7
H.C.F. (70, 105, 175)
= 5 × 7
= 35
(h) 91, 112, 49
Solution:
Prime factorization of 91
= 7 × 13
Prime factorization of 112
= 2 × 2 × 2 × 2 × 7
Prime factorization of 49
= 7 × 7
H.C.F. (91, 112, 49) = 7
(i) 18, 54, 81
Solution:
Prime factorization of 18
= 2 × 3 × 3
Prime factorization of 54
= 2 × 3 × 3 × 3
Prime factorization of 81
= 3 × 3 × 3 × 3
H.C.F. = 3 × 3 = 9
(j) 12, 45, 75
Solution:
Prime factorization of 12
= 2 × 2 × 3
Prime factorization of 45
= 3 × 3 × 5
Prime factorization of 75
= 3 x 5 x 5
H.C.F. = 1 × 3
= 3
Q2. What is the H.C.F. of two consecutive:
(a) numbers?
(b) even numbers?
(c) odd numbers?
Solution:
(a) H.C.F. of two consecutive numbers be 1.
(b) H.C.F. of two consecutive even numbers be 2.
(c) H.C.F. of two consecutive odd numbers be 1.
Q3. H.C.F. of co-prime numbers 4 and 15 was found as follows by factorization:
4 = 2 × 2 and
15 = 3 × 5 since there is no common prime factor, so H.C.F. of 4 and 15 is 0. Is the answer correct? If not, what is the correct H.C.F.?
Solution: No. The correct H.C.F. is 1.
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