Friendly Numbers

by John McConnell

"After Jacob had spent the night there, he chose some animals as gifts for Esau; two hundred female goats and twenty males, two hundred female sheep and twenty males."

Gen. 32: 13,14.


Esau was plenty angry, in fact he was furious. About fifteen years before, his brother Jacob had swindled him out of his birthright and patriarchal blessing. It happened one day when he came back from a hunting expedition, and he was tired and hungry. Jacob had cooked up a pot of red beans and lentils, called pottage, and it smelled mighty good to hungry Esau. So Esau sold his birthright to Jacob for a mess of pottage. This birthright was always given to the eldest son. Subsequently, Jacob and his mother, Rebekah, conspired to deceive poor old blind Isaac into bestowing on Jacob the patriarchal blessing, which rightfully belonged to Esau. When Esau woke up and realized what had happened, he was ready to kill his brother, and Jacob fled from the country for his life. After almost fifteen years he was now on his way back home with his two wives, twelve sons, servants, and flocks of sheep, goats, and cattle. When he heard that Esau had mustered an army of four hundred men and was on his way to meet him, he was very frightened; he divided his retinue into two groups, and then sent servants with a peace offering of 220 goats and 220 sheep

This peace offering had an unexpected effect on Esau. When Jacob saw Esau approaching with his four hundred men, he bowed himself to the ground seven times, and then to his complete surprise, Esau ran to meet him, embraced him, fell on his neck, and kissed him. Unless you knew about the significance of the number 220, you would not understand why Esau did this. Mathematicians love to crunch numbers; there are odd numbers, even numbers, whole numbers, integers, decimals, real numbers, imaginary numbers, rational numbers, irrational numbers, positive numbers, negative numbers, prime numbers, perfect numbers, and friendly numbers. Friendly numbers are two numbers each of whose divisors add up to the other number. The smallest combination of friendly numbers is 220 & 284. The eleven divisors of 220 (1,2,4,5,10,11,20,22,44,55, 110) add up to 284. Similarly, the divisors of 284 (1,2,4,71,142) add up to 220. Esau and Jacob must have known about friendly numbers because Esau got the message.

This story is an example of what can be accomplished by being friendly, and as Christians we should go out of our way to be friendly. We are told that we should not hold a grudge, that we should not seek revenge when we are wronged, that we should turn the other cheek, that we should go the second mile, that we should give a soft answer to wrath. We may not have 220 goats or sheep, and most people wouldn't understand the message even if we did, but a smile instead of a frown will go a long way toward turning animosity into friendship and in delivering the same message as Jacob's "friendly numbers."


© 2007 John McConnell
This page last updated: Thursday August 23 2007

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