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 341, 651, 748 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 341, 651, 748 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 341, 651, 748 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 341, 651, 748 is 1.
HCF(341, 651, 748) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 341, 651, 748 is 1.
Step 1: Since 651 > 341, we apply the division lemma to 651 and 341, to get
651 = 341 x 1 + 310
Step 2: Since the reminder 341 ≠ 0, we apply division lemma to 310 and 341, to get
341 = 310 x 1 + 31
Step 3: We consider the new divisor 310 and the new remainder 31, and apply the division lemma to get
310 = 31 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 31, the HCF of 341 and 651 is 31
Notice that 31 = HCF(310,31) = HCF(341,310) = HCF(651,341) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 748 > 31, we apply the division lemma to 748 and 31, to get
748 = 31 x 24 + 4
Step 2: Since the reminder 31 ≠ 0, we apply division lemma to 4 and 31, to get
31 = 4 x 7 + 3
Step 3: We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 31 and 748 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(31,4) = HCF(748,31) .
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 341, 651, 748?
Answer: HCF of 341, 651, 748 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 341, 651, 748 using Euclid's Algorithm?
Answer: For arbitrary numbers 341, 651, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.