Highest Common Factor of 7974, 5554 using Euclid's algorithm
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 7974, 5554 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7974, 5554 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 7974, 5554 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 7974, 5554 is 2.
HCF(7974, 5554) = 2
HCF of 7974, 5554 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7974, 5554 is 2.
Highest Common Factor of 7974,5554 is 2
Step 1: Since 7974 > 5554, we apply the division lemma to 7974 and 5554, to get
7974 = 5554 x 1 + 2420
Step 2: Since the reminder 5554 ≠ 0, we apply division lemma to 2420 and 5554, to get
5554 = 2420 x 2 + 714
Step 3: We consider the new divisor 2420 and the new remainder 714, and apply the division lemma to get
2420 = 714 x 3 + 278
We consider the new divisor 714 and the new remainder 278,and apply the division lemma to get
714 = 278 x 2 + 158
We consider the new divisor 278 and the new remainder 158,and apply the division lemma to get
278 = 158 x 1 + 120
We consider the new divisor 158 and the new remainder 120,and apply the division lemma to get
158 = 120 x 1 + 38
We consider the new divisor 120 and the new remainder 38,and apply the division lemma to get
120 = 38 x 3 + 6
We consider the new divisor 38 and the new remainder 6,and apply the division lemma to get
38 = 6 x 6 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7974 and 5554 is 2
Notice that 2 = HCF(6,2) = HCF(38,6) = HCF(120,38) = HCF(158,120) = HCF(278,158) = HCF(714,278) = HCF(2420,714) = HCF(5554,2420) = HCF(7974,5554) .
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Frequently Asked Questions on HCF of 7974, 5554 using Euclid's Algorithm
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 7974, 5554?
Answer: HCF of 7974, 5554 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7974, 5554 using Euclid's Algorithm?
Answer: For arbitrary numbers 7974, 5554 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.