Highest Common Factor of 992, 640, 762 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 992, 640, 762 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 992, 640, 762 is 2 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 992, 640, 762 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 992, 640, 762 is 2.
HCF(992, 640, 762) = 2
HCF of 992, 640, 762 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 992, 640, 762 is 2.
Highest Common Factor of 992,640,762 is 2
Step 1: Since 992 > 640, we apply the division lemma to 992 and 640, to get
992 = 640 x 1 + 352
Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 352 and 640, to get
640 = 352 x 1 + 288
Step 3: We consider the new divisor 352 and the new remainder 288, and apply the division lemma to get
352 = 288 x 1 + 64
We consider the new divisor 288 and the new remainder 64,and apply the division lemma to get
288 = 64 x 4 + 32
We consider the new divisor 64 and the new remainder 32,and apply the division lemma to get
64 = 32 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 992 and 640 is 32
Notice that 32 = HCF(64,32) = HCF(288,64) = HCF(352,288) = HCF(640,352) = HCF(992,640) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 762 > 32, we apply the division lemma to 762 and 32, to get
762 = 32 x 23 + 26
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 26 and 32, to get
32 = 26 x 1 + 6
Step 3: We consider the new divisor 26 and the new remainder 6, and apply the division lemma to get
26 = 6 x 4 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 32 and 762 is 2
Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(32,26) = HCF(762,32) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 992, 640, 762 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 992, 640, 762?
Answer: HCF of 992, 640, 762 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 992, 640, 762 using Euclid's Algorithm?
Answer: For arbitrary numbers 992, 640, 762 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.