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 510, 942, 772 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 942, 772 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 510, 942, 772 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 510, 942, 772 is 2.
HCF(510, 942, 772) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 510, 942, 772 is 2.
Step 1: Since 942 > 510, we apply the division lemma to 942 and 510, to get
942 = 510 x 1 + 432
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 432 and 510, to get
510 = 432 x 1 + 78
Step 3: We consider the new divisor 432 and the new remainder 78, and apply the division lemma to get
432 = 78 x 5 + 42
We consider the new divisor 78 and the new remainder 42,and apply the division lemma to get
78 = 42 x 1 + 36
We consider the new divisor 42 and the new remainder 36,and apply the division lemma to get
42 = 36 x 1 + 6
We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 510 and 942 is 6
Notice that 6 = HCF(36,6) = HCF(42,36) = HCF(78,42) = HCF(432,78) = HCF(510,432) = HCF(942,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 772 > 6, we apply the division lemma to 772 and 6, to get
772 = 6 x 128 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 772 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(772,6) .
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 510, 942, 772?
Answer: HCF of 510, 942, 772 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 942, 772 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 942, 772 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.