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 946, 640, 660 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 946, 640, 660 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 946, 640, 660 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 946, 640, 660 is 2.
HCF(946, 640, 660) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 946, 640, 660 is 2.
Step 1: Since 946 > 640, we apply the division lemma to 946 and 640, to get
946 = 640 x 1 + 306
Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 306 and 640, to get
640 = 306 x 2 + 28
Step 3: We consider the new divisor 306 and the new remainder 28, and apply the division lemma to get
306 = 28 x 10 + 26
We consider the new divisor 28 and the new remainder 26,and apply the division lemma to get
28 = 26 x 1 + 2
We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 946 and 640 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(306,28) = HCF(640,306) = HCF(946,640) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 660 > 2, we apply the division lemma to 660 and 2, to get
660 = 2 x 330 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 660 is 2
Notice that 2 = HCF(660,2) .
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 946, 640, 660?
Answer: HCF of 946, 640, 660 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 946, 640, 660 using Euclid's Algorithm?
Answer: For arbitrary numbers 946, 640, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.