The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers upto 100.
Solution and Explanation
Pairs of prime numbers that have the same digits, like 13 and 31, are called "permutable primes" or "anagrammatic primes."
Here are some pairs of permutable primes up to 100:
(a) 17 and 71
(b) 37 and 73
(c) 79 and 97
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Concepts Used:
Highest Common Factor - Playing With Numbers
The highest common factor (HCF) is the largest number that divides two or more given numbers without leaving a remainder. It is also known as the greatest common divisor (GCD). To find the HCF of two or more numbers, we need to factorize each number into its prime factors and then identify the common factors. The HCF is then obtained by multiplying the common factors.
For example, to find the HCF of 12 and 18, we first factorize the numbers into their prime factors: 12 = 2 × 2 × 3 and 18 = 2 × 3 × 3. The common factors are 2 and 3, so the HCF is 2 × 3 = 6.
The concept of HCF is often used in various mathematical applications, such as simplifying fractions and finding equivalent fractions. For example, to simplify the fraction 24/36, we can find the HCF of 24 and 36, which is 12. We can then divide both the numerator and denominator of the fraction by 12 to get the simplified form, which is 2/3.
HCF is also used in solving problems related to ratios and proportions. For instance, in a group of 60 students, 24 are boys and the rest are girls. What is the maximum number of equal groups that can be formed with these students? To solve this, we first find the HCF of 24 and 36 (the number of girls). The HCF is 12, which means that we can form a maximum of 5 groups of 12 students each, with 4 boys and 8 girls in each group.
Overall, understanding the concept of HCF and how to find it is important in many mathematical applications, especially in solving problems related to fractions, ratios, and proportions.