Question: Which Of The Following Pairs Of Numbers Is Amicable *?

Are 60 and 84 Amicable numbers?

Amicable Numbers The Greeks considered the pair of numbers 220 and 284 to be amicable or friendly numbers because the sum of the proper divisors of one of the numbers is the other number.

a.

60 and 84 are amicable numbers..

What is an example of a friendly number?

An addition/subtraction strategy that uses a number that is easy to work from, typically 10 or a multiple of 10. For example, to solve 16 – 9, one might recognize that the friendly number 10 is 6 less than 16, then count down 1 more to 9 to find that the difference is 7.

What is a friendly pair in math?

In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself. Two numbers with the same “abundancy” form a friendly pair; n numbers with the same “abundancy” form a friendly n-tuple.

Are 1184 and 1210 amicable numbers?

Almost perfect number pairs are pairs of numbers that equal the sum of their partner’s divisors. For example, 1184 and 1210 are an almost perfect number pair. 1184 = 1+2+5+10+11+22+55+110+121+242+605, the sum of the divisors of 1210. … The set of numbers requested, above, are amicable numbers if they come in pairs.

What are the first 3 perfect numbers?

The first few perfect numbers are 6, 28, 496 and 8128 (sequence A000396 in the OEIS).

What are special numbers?

Special Numbers in Java are ones whose sum of factorials of digits is equal to the number itself. It can be an N digit number. The program has to first break the number into its corresponding digits and calculate their factorials. … If the sum matches the original number then the number is called to be a Special number.

What are amicable numbers used for?

…“amicable numbers”: two numbers are amicable if each is equal to the sum of the proper divisors of the other (for example, 220 and 284). Attributing virtues such as friendship and justice to numbers was characteristic of the Pythagoreans at all times.

Why is 28 the perfect number?

A number is perfect if all of its factors, including 1 but excluding itself, perfectly add up to the number you began with. 6, for example, is perfect, because its factors — 3, 2, and 1 — all sum up to 6. 28 is perfect too: 14, 7, 4, 2, and 1 add up to 28.

Is 496 a amicable number?

A perfect number is a cycle of length 1 of s, i.e., a number whose positive divisors (except for itself) sum to itself. For example, 6 is perfect (1+2+3=6), and in fact 6 is the smallest perfect number. The next two perfect numbers are 28 (1+2+4+7+14=28) and 496 (1+2+4+8+16+31+62+124+248=496).

What does the number 28 symbolize?

The number 28 symbolizes balance, harmony, service to others, empathy, adaptability, divine life purpose and soul mission, manifestation of wealth, prosperity and abundance, solving problems, achieving success, knowledge, inner wisdom, the Universal Spiritual Law of Karma, partnerships, authority, finances, leadership, …

Why is three the perfect number?

Three is the smallest number we need to create a pattern, the perfect combination of brevity and rhythm. … It’s a principle captured neatly in the Latin phrase omne trium perfectum: everything that comes in threes is perfect, or, every set of three is complete.

WHY IS 496 a perfect number?

Also related to its being a perfect number, 496 is a harmonic divisor number, since the number of proper divisors of 496 divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496, (the harmonic mean), yields an integer, 5 in this case. … It is the largest happy number less than 500.

IS 496 a perfect square Why?

Is 496 a perfect square number? A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 496 is about 22.271. Thus, the square root of 496 is not an integer, and therefore 496 is not a square number.

How many amicable numbers are there?

Altogether there are 42 pairs of amicable numbers below 106.

What is the most special number?

6174 is a harshad number, since it is divisible by the sum of its digits: 6174 is a 7-smooth number, i.e. none of its prime factors are greater than 7.

How do I know if a number is amicable?

Two numbers are said to be amicable if each number is the sum of the proper divisors of the other. A proper divisor of a number is any divisor of the number except the number itself. For example, the proper divisor of 12 are 1, 2, 3, 4, and 6.

Is 496 perfect square?

496 is not a perfect square.

Is 6 an amicable number?

Amicable numbers are two different numbers related in such a way that the sum of the proper divisors of each is equal to the other number. … (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.)