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 336, 3290, 7874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 336, 3290, 7874 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 336, 3290, 7874 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 336, 3290, 7874 is 2.
HCF(336, 3290, 7874) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 336, 3290, 7874 is 2.
Step 1: Since 3290 > 336, we apply the division lemma to 3290 and 336, to get
3290 = 336 x 9 + 266
Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 266 and 336, to get
336 = 266 x 1 + 70
Step 3: We consider the new divisor 266 and the new remainder 70, and apply the division lemma to get
266 = 70 x 3 + 56
We consider the new divisor 70 and the new remainder 56,and apply the division lemma to get
70 = 56 x 1 + 14
We consider the new divisor 56 and the new remainder 14,and apply the division lemma to get
56 = 14 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 336 and 3290 is 14
Notice that 14 = HCF(56,14) = HCF(70,56) = HCF(266,70) = HCF(336,266) = HCF(3290,336) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7874 > 14, we apply the division lemma to 7874 and 14, to get
7874 = 14 x 562 + 6
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 6 and 14, to get
14 = 6 x 2 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 7874 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(7874,14) .
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 336, 3290, 7874?
Answer: HCF of 336, 3290, 7874 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 336, 3290, 7874 using Euclid's Algorithm?
Answer: For arbitrary numbers 336, 3290, 7874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.