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 930, 7090, 7046 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 930, 7090, 7046 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 930, 7090, 7046 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 930, 7090, 7046 is 2.
HCF(930, 7090, 7046) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 930, 7090, 7046 is 2.
Step 1: Since 7090 > 930, we apply the division lemma to 7090 and 930, to get
7090 = 930 x 7 + 580
Step 2: Since the reminder 930 ≠ 0, we apply division lemma to 580 and 930, to get
930 = 580 x 1 + 350
Step 3: We consider the new divisor 580 and the new remainder 350, and apply the division lemma to get
580 = 350 x 1 + 230
We consider the new divisor 350 and the new remainder 230,and apply the division lemma to get
350 = 230 x 1 + 120
We consider the new divisor 230 and the new remainder 120,and apply the division lemma to get
230 = 120 x 1 + 110
We consider the new divisor 120 and the new remainder 110,and apply the division lemma to get
120 = 110 x 1 + 10
We consider the new divisor 110 and the new remainder 10,and apply the division lemma to get
110 = 10 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 930 and 7090 is 10
Notice that 10 = HCF(110,10) = HCF(120,110) = HCF(230,120) = HCF(350,230) = HCF(580,350) = HCF(930,580) = HCF(7090,930) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7046 > 10, we apply the division lemma to 7046 and 10, to get
7046 = 10 x 704 + 6
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 6 and 10, to get
10 = 6 x 1 + 4
Step 3: 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 10 and 7046 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(7046,10) .
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 930, 7090, 7046?
Answer: HCF of 930, 7090, 7046 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 930, 7090, 7046 using Euclid's Algorithm?
Answer: For arbitrary numbers 930, 7090, 7046 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.