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 496, 6762, 1891 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 496, 6762, 1891 is 1 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 496, 6762, 1891 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 496, 6762, 1891 is 1.
HCF(496, 6762, 1891) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 496, 6762, 1891 is 1.
Step 1: Since 6762 > 496, we apply the division lemma to 6762 and 496, to get
6762 = 496 x 13 + 314
Step 2: Since the reminder 496 ≠ 0, we apply division lemma to 314 and 496, to get
496 = 314 x 1 + 182
Step 3: We consider the new divisor 314 and the new remainder 182, and apply the division lemma to get
314 = 182 x 1 + 132
We consider the new divisor 182 and the new remainder 132,and apply the division lemma to get
182 = 132 x 1 + 50
We consider the new divisor 132 and the new remainder 50,and apply the division lemma to get
132 = 50 x 2 + 32
We consider the new divisor 50 and the new remainder 32,and apply the division lemma to get
50 = 32 x 1 + 18
We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get
32 = 18 x 1 + 14
We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 496 and 6762 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(50,32) = HCF(132,50) = HCF(182,132) = HCF(314,182) = HCF(496,314) = HCF(6762,496) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1891 > 2, we apply the division lemma to 1891 and 2, to get
1891 = 2 x 945 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 1891 is 1
Notice that 1 = HCF(2,1) = HCF(1891,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 496, 6762, 1891?
Answer: HCF of 496, 6762, 1891 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 496, 6762, 1891 using Euclid's Algorithm?
Answer: For arbitrary numbers 496, 6762, 1891 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.