HCF of 867 and 255 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 867 and 255.

No further division can be done.

Hence, HCF (867, 255) = 51

📝 Explanation:

Denominator has prime factor 7 → recurring decimal.

To solve this question, recall that:

Prime numbers are whole numbers whose only factors are 1 and the number itself.

Composite numbers are positive integers that have factors other than 1 and themselves.

7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = 5 × (7 × 6 × 4 × 3 × 2 × 1 + 1)

= 5 × (1008 + 1)

= 5 × 1009 × 1

1009 cannot be factorized further. Therefore, the given expression has 5,1009 and 1 as its factors. Hence, it is a composite number.

77/210 = (7 × 11)/(30 × 7) = 11/30

30 = 2 × 3 × 5

Since the denominator is not of form 2m × 5n and it also has 3 as its factor, the decimal expansion of 77/210 is non-terminating repeating.

LCM × HCF = Product of the two numbers

Prime factors of 26 = 2 × 13

Prime factors of 91 = 7 × 13

HCF of 26 and 91 = 13

LCM of 26 and 91 = 2 × 7 × 13

= 14 × 13

= 182

Product of these two numbers = 26 × 91 = 2366

LCM × HCF = 182 × 13 = 2366

Thus, the product of two numbers = LCM × HCF

📝 Explanation:

Sum of two irrational numbers like √2 and √5 is irrational.

If the denominator of the fraction is made up of only prime factors of 2 or 5, then the decimal will be terminating. Otherwise, it will be non-terminating recurring.

The denominator of 17/21 is 21, which has prime factors of 3 x 7. Since the denominator has prime factors other than 2 or 5, the decimal will be non-terminating recurring.

The cube of a number cannot be of the form (4m+2) or (9m+2), where m is an integer.

HCF of 196 and 38220 by Long Division Method 

Step 1: Divide 38220 (larger number) by 196 (smaller number).

Step 2: Since the remainder = 0, the divisor (196) is the HCF of 196 and 38220.

The corresponding divisor (196) is the HCF of 196 and 38220.