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 3756, 7088, 74062 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3756, 7088, 74062 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 3756, 7088, 74062 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 3756, 7088, 74062 is 2.
HCF(3756, 7088, 74062) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3756, 7088, 74062 is 2.
Step 1: Since 7088 > 3756, we apply the division lemma to 7088 and 3756, to get
7088 = 3756 x 1 + 3332
Step 2: Since the reminder 3756 ≠ 0, we apply division lemma to 3332 and 3756, to get
3756 = 3332 x 1 + 424
Step 3: We consider the new divisor 3332 and the new remainder 424, and apply the division lemma to get
3332 = 424 x 7 + 364
We consider the new divisor 424 and the new remainder 364,and apply the division lemma to get
424 = 364 x 1 + 60
We consider the new divisor 364 and the new remainder 60,and apply the division lemma to get
364 = 60 x 6 + 4
We consider the new divisor 60 and the new remainder 4,and apply the division lemma to get
60 = 4 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 3756 and 7088 is 4
Notice that 4 = HCF(60,4) = HCF(364,60) = HCF(424,364) = HCF(3332,424) = HCF(3756,3332) = HCF(7088,3756) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74062 > 4, we apply the division lemma to 74062 and 4, to get
74062 = 4 x 18515 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 74062 is 2
Notice that 2 = HCF(4,2) = HCF(74062,4) .
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 3756, 7088, 74062?
Answer: HCF of 3756, 7088, 74062 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3756, 7088, 74062 using Euclid's Algorithm?
Answer: For arbitrary numbers 3756, 7088, 74062 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.