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 837, 945, 460 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 837, 945, 460 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 837, 945, 460 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 837, 945, 460 is 1.
HCF(837, 945, 460) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 837, 945, 460 is 1.
Step 1: Since 945 > 837, we apply the division lemma to 945 and 837, to get
945 = 837 x 1 + 108
Step 2: Since the reminder 837 ≠ 0, we apply division lemma to 108 and 837, to get
837 = 108 x 7 + 81
Step 3: We consider the new divisor 108 and the new remainder 81, and apply the division lemma to get
108 = 81 x 1 + 27
We consider the new divisor 81 and the new remainder 27, and apply the division lemma to get
81 = 27 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 837 and 945 is 27
Notice that 27 = HCF(81,27) = HCF(108,81) = HCF(837,108) = HCF(945,837) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 460 > 27, we apply the division lemma to 460 and 27, to get
460 = 27 x 17 + 1
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 1 and 27, to get
27 = 1 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 27 and 460 is 1
Notice that 1 = HCF(27,1) = HCF(460,27) .
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 837, 945, 460?
Answer: HCF of 837, 945, 460 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 837, 945, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 837, 945, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.