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 780, 276, 975 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 780, 276, 975 is 3 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 780, 276, 975 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 780, 276, 975 is 3.
HCF(780, 276, 975) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 780, 276, 975 is 3.
Step 1: Since 780 > 276, we apply the division lemma to 780 and 276, to get
780 = 276 x 2 + 228
Step 2: Since the reminder 276 ≠ 0, we apply division lemma to 228 and 276, to get
276 = 228 x 1 + 48
Step 3: We consider the new divisor 228 and the new remainder 48, and apply the division lemma to get
228 = 48 x 4 + 36
We consider the new divisor 48 and the new remainder 36,and apply the division lemma to get
48 = 36 x 1 + 12
We consider the new divisor 36 and the new remainder 12,and apply the division lemma to get
36 = 12 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 780 and 276 is 12
Notice that 12 = HCF(36,12) = HCF(48,36) = HCF(228,48) = HCF(276,228) = HCF(780,276) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 975 > 12, we apply the division lemma to 975 and 12, to get
975 = 12 x 81 + 3
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 3 and 12, to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 12 and 975 is 3
Notice that 3 = HCF(12,3) = HCF(975,12) .
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 780, 276, 975?
Answer: HCF of 780, 276, 975 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 780, 276, 975 using Euclid's Algorithm?
Answer: For arbitrary numbers 780, 276, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.