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 456, 756, 325 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 456, 756, 325 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 456, 756, 325 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 456, 756, 325 is 1.
HCF(456, 756, 325) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 456, 756, 325 is 1.
Step 1: Since 756 > 456, we apply the division lemma to 756 and 456, to get
756 = 456 x 1 + 300
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 300 and 456, to get
456 = 300 x 1 + 156
Step 3: We consider the new divisor 300 and the new remainder 156, and apply the division lemma to get
300 = 156 x 1 + 144
We consider the new divisor 156 and the new remainder 144,and apply the division lemma to get
156 = 144 x 1 + 12
We consider the new divisor 144 and the new remainder 12,and apply the division lemma to get
144 = 12 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 456 and 756 is 12
Notice that 12 = HCF(144,12) = HCF(156,144) = HCF(300,156) = HCF(456,300) = HCF(756,456) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 325 > 12, we apply the division lemma to 325 and 12, to get
325 = 12 x 27 + 1
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 1 and 12, to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 12 and 325 is 1
Notice that 1 = HCF(12,1) = HCF(325,12) .
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 456, 756, 325?
Answer: HCF of 456, 756, 325 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 456, 756, 325 using Euclid's Algorithm?
Answer: For arbitrary numbers 456, 756, 325 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.