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 688, 3042, 8001 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 3042, 8001 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 688, 3042, 8001 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 688, 3042, 8001 is 1.
HCF(688, 3042, 8001) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 688, 3042, 8001 is 1.
Step 1: Since 3042 > 688, we apply the division lemma to 3042 and 688, to get
3042 = 688 x 4 + 290
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 290 and 688, to get
688 = 290 x 2 + 108
Step 3: We consider the new divisor 290 and the new remainder 108, and apply the division lemma to get
290 = 108 x 2 + 74
We consider the new divisor 108 and the new remainder 74,and apply the division lemma to get
108 = 74 x 1 + 34
We consider the new divisor 74 and the new remainder 34,and apply the division lemma to get
74 = 34 x 2 + 6
We consider the new divisor 34 and the new remainder 6,and apply the division lemma to get
34 = 6 x 5 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 688 and 3042 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(34,6) = HCF(74,34) = HCF(108,74) = HCF(290,108) = HCF(688,290) = HCF(3042,688) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8001 > 2, we apply the division lemma to 8001 and 2, to get
8001 = 2 x 4000 + 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 8001 is 1
Notice that 1 = HCF(2,1) = HCF(8001,2) .
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 688, 3042, 8001?
Answer: HCF of 688, 3042, 8001 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 3042, 8001 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 3042, 8001 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.