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 351, 414, 860 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 351, 414, 860 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 351, 414, 860 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 351, 414, 860 is 1.
HCF(351, 414, 860) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 351, 414, 860 is 1.
Step 1: Since 414 > 351, we apply the division lemma to 414 and 351, to get
414 = 351 x 1 + 63
Step 2: Since the reminder 351 ≠ 0, we apply division lemma to 63 and 351, to get
351 = 63 x 5 + 36
Step 3: We consider the new divisor 63 and the new remainder 36, and apply the division lemma to get
63 = 36 x 1 + 27
We consider the new divisor 36 and the new remainder 27,and apply the division lemma to get
36 = 27 x 1 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 351 and 414 is 9
Notice that 9 = HCF(27,9) = HCF(36,27) = HCF(63,36) = HCF(351,63) = HCF(414,351) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 860 > 9, we apply the division lemma to 860 and 9, to get
860 = 9 x 95 + 5
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 5 and 9, to get
9 = 5 x 1 + 4
Step 3: We consider the new divisor 5 and the new remainder 4, and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 860 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(860,9) .
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 351, 414, 860?
Answer: HCF of 351, 414, 860 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 351, 414, 860 using Euclid's Algorithm?
Answer: For arbitrary numbers 351, 414, 860 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.