Highest Common Factor of 1981, 462 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 1981, 462 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 1981, 462 is 7 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 1981, 462 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 1981, 462 is 7.
HCF(1981, 462) = 7
HCF of 1981, 462 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1981, 462 is 7.
Highest Common Factor of 1981,462 is 7
Step 1: Since 1981 > 462, we apply the division lemma to 1981 and 462, to get
1981 = 462 x 4 + 133
Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 133 and 462, to get
462 = 133 x 3 + 63
Step 3: We consider the new divisor 133 and the new remainder 63, and apply the division lemma to get
133 = 63 x 2 + 7
We consider the new divisor 63 and the new remainder 7, and apply the division lemma to get
63 = 7 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 1981 and 462 is 7
Notice that 7 = HCF(63,7) = HCF(133,63) = HCF(462,133) = HCF(1981,462) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1981, 462 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 1981, 462?
Answer: HCF of 1981, 462 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1981, 462 using Euclid's Algorithm?
Answer: For arbitrary numbers 1981, 462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.