Highest Common Factor of 1050, 8109, 46938 using Euclid's algorithm
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 1050, 8109, 46938 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1050, 8109, 46938 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 1050, 8109, 46938 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 1050, 8109, 46938 is 3.
HCF(1050, 8109, 46938) = 3
HCF of 1050, 8109, 46938 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1050, 8109, 46938 is 3.
Highest Common Factor of 1050,8109,46938 is 3
Step 1: Since 8109 > 1050, we apply the division lemma to 8109 and 1050, to get
8109 = 1050 x 7 + 759
Step 2: Since the reminder 1050 ≠ 0, we apply division lemma to 759 and 1050, to get
1050 = 759 x 1 + 291
Step 3: We consider the new divisor 759 and the new remainder 291, and apply the division lemma to get
759 = 291 x 2 + 177
We consider the new divisor 291 and the new remainder 177,and apply the division lemma to get
291 = 177 x 1 + 114
We consider the new divisor 177 and the new remainder 114,and apply the division lemma to get
177 = 114 x 1 + 63
We consider the new divisor 114 and the new remainder 63,and apply the division lemma to get
114 = 63 x 1 + 51
We consider the new divisor 63 and the new remainder 51,and apply the division lemma to get
63 = 51 x 1 + 12
We consider the new divisor 51 and the new remainder 12,and apply the division lemma to get
51 = 12 x 4 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1050 and 8109 is 3
Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(63,51) = HCF(114,63) = HCF(177,114) = HCF(291,177) = HCF(759,291) = HCF(1050,759) = HCF(8109,1050) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 46938 > 3, we apply the division lemma to 46938 and 3, to get
46938 = 3 x 15646 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 46938 is 3
Notice that 3 = HCF(46938,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1050, 8109, 46938 using Euclid's Algorithm
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 1050, 8109, 46938?
Answer: HCF of 1050, 8109, 46938 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1050, 8109, 46938 using Euclid's Algorithm?
Answer: For arbitrary numbers 1050, 8109, 46938 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.