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 414, 549, 970, 44 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 549, 970, 44 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 414, 549, 970, 44 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 414, 549, 970, 44 is 1.
HCF(414, 549, 970, 44) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 549, 970, 44 is 1.
Step 1: Since 549 > 414, we apply the division lemma to 549 and 414, to get
549 = 414 x 1 + 135
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 135 and 414, to get
414 = 135 x 3 + 9
Step 3: We consider the new divisor 135 and the new remainder 9, and apply the division lemma to get
135 = 9 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 414 and 549 is 9
Notice that 9 = HCF(135,9) = HCF(414,135) = HCF(549,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 970 > 9, we apply the division lemma to 970 and 9, to get
970 = 9 x 107 + 7
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 7 and 9, to get
9 = 7 x 1 + 2
Step 3: We consider the new divisor 7 and the new remainder 2, and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 970 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(970,9) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 44 > 1, we apply the division lemma to 44 and 1, to get
44 = 1 x 44 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 44 is 1
Notice that 1 = HCF(44,1) .
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 414, 549, 970, 44?
Answer: HCF of 414, 549, 970, 44 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 549, 970, 44 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 549, 970, 44 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.