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 8037, 7263, 66540 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8037, 7263, 66540 is 3 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 8037, 7263, 66540 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 8037, 7263, 66540 is 3.
HCF(8037, 7263, 66540) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8037, 7263, 66540 is 3.
Step 1: Since 8037 > 7263, we apply the division lemma to 8037 and 7263, to get
8037 = 7263 x 1 + 774
Step 2: Since the reminder 7263 ≠ 0, we apply division lemma to 774 and 7263, to get
7263 = 774 x 9 + 297
Step 3: We consider the new divisor 774 and the new remainder 297, and apply the division lemma to get
774 = 297 x 2 + 180
We consider the new divisor 297 and the new remainder 180,and apply the division lemma to get
297 = 180 x 1 + 117
We consider the new divisor 180 and the new remainder 117,and apply the division lemma to get
180 = 117 x 1 + 63
We consider the new divisor 117 and the new remainder 63,and apply the division lemma to get
117 = 63 x 1 + 54
We consider the new divisor 63 and the new remainder 54,and apply the division lemma to get
63 = 54 x 1 + 9
We consider the new divisor 54 and the new remainder 9,and apply the division lemma to get
54 = 9 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 8037 and 7263 is 9
Notice that 9 = HCF(54,9) = HCF(63,54) = HCF(117,63) = HCF(180,117) = HCF(297,180) = HCF(774,297) = HCF(7263,774) = HCF(8037,7263) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66540 > 9, we apply the division lemma to 66540 and 9, to get
66540 = 9 x 7393 + 3
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 66540 is 3
Notice that 3 = HCF(9,3) = HCF(66540,9) .
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 8037, 7263, 66540?
Answer: HCF of 8037, 7263, 66540 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8037, 7263, 66540 using Euclid's Algorithm?
Answer: For arbitrary numbers 8037, 7263, 66540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.