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 372, 846, 890 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 372, 846, 890 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 372, 846, 890 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 372, 846, 890 is 2.
HCF(372, 846, 890) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 372, 846, 890 is 2.
Step 1: Since 846 > 372, we apply the division lemma to 846 and 372, to get
846 = 372 x 2 + 102
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 102 and 372, to get
372 = 102 x 3 + 66
Step 3: We consider the new divisor 102 and the new remainder 66, and apply the division lemma to get
102 = 66 x 1 + 36
We consider the new divisor 66 and the new remainder 36,and apply the division lemma to get
66 = 36 x 1 + 30
We consider the new divisor 36 and the new remainder 30,and apply the division lemma to get
36 = 30 x 1 + 6
We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 372 and 846 is 6
Notice that 6 = HCF(30,6) = HCF(36,30) = HCF(66,36) = HCF(102,66) = HCF(372,102) = HCF(846,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 890 > 6, we apply the division lemma to 890 and 6, to get
890 = 6 x 148 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 890 is 2
Notice that 2 = HCF(6,2) = HCF(890,6) .
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 372, 846, 890?
Answer: HCF of 372, 846, 890 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 372, 846, 890 using Euclid's Algorithm?
Answer: For arbitrary numbers 372, 846, 890 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.