Make a general statement about the HCF for the following pairs of numbers. Class 7

Make a general statement about the HCF for the following pairs of numbers. Class 7

Question 1.

Make a general statement about the HCF for the following pairs of numbers. You could consider examples before coming up with general statements. Look for possible explanations of why they hold. Class 7

(a) Two consecutive even numbers

(b) Two consecutive odd numbers

(c) Two even numbers

(d) Two consecutive numbers

(e) Two co-prime numbers

Share your observations with the class.

Solution:

(a) Their HCF will be 2.

(b) Their HCF will be 1.

(c) Their HCF will be even.

(d) Their HCF will be 1.

(e) Their HCF will be 1.

Question 2.

The LCM of 3 and 24 is 24 (it is one of the two given numbers). Class 7

(a) Find more such number pairs where the LCM is one of the two numbers.

(b) Make a general statement about such- numbers. Describe such number pairs using algebra.

Solution:

(a) More such numbers are : 4 and 12; 9 and 45.

(b) Bigger number is the multiple of smaller number.

Algebraic form : a and pa.

pa is the LCM of a.